The announcement by the Blazers on Monday came less than an hour after the Clippers revealed that they and Olshey had decided to part ways.
Last season, Olshey oversaw a major retooling of the Clippers that included signing All-Star point guard Chris Paul in December as part of the biggest trade in franchise history. In the same six-day span, Olshey signed All-Stars Caron Butler and Chauncey Billups, and re-signed DeAndre Jordan.
The Clippers finished 40-26 and reached the second round of the playoffs.
"I am very grateful for the opportunity to become a part of this successful franchise," Olshey said in a statement released by the Blazers. "Portland is a great basketball city with a rich tradition, an incredible fan base and committed leadership. I'm joining an organization that has a strong foundation and a bright future."
The Blazers have been operating under interim GM Chad Buchanan for the past year. Buchanan, the team's director of college scouting, took over when the team fired Rich Cho after about 10 months on the job.
Former New Orleans general manager and coach Jeff Bower, Indiana Pacers general manager David Morway and Philadelphia 76ers senior vice president of basketball operations Tony DiLeo were among the finalists for the job.
Olshey becomes the 10th general manager in Blazers history.
"Neil is someone we've had on our radar for quite a while. Over the past two seasons he has demonstrated success in constructing a roster, managing salary cap and evaluating player talent," Blazers President Larry Miller said in a statement. "We feel very fortunate to have him in Portland and are thrilled about what this means for the future."
The Blazers say they are planning a news conference for Tuesday.
The Clippers had announced on Friday that the team had reached an agreement in principle to a new agreement with Olshey, who had been working without a contract since October 2011. A media conference call had initially been scheduled for Monday afternoon by the Clippers, but final negotiations stalled as the Trail Blazers stepped in to secure Olshey's services, according to sources.
"Circumstances have obviously undergone some movement since our announcement Friday. In light of that, we want to wish Neil well and acknowledge his contributions during the time he spent with the Clippers," said Clippers' president Andy Roeser.
Olshey had previously interviewed for the position in Portland last September during the work stoppage.
The 47-year-old Olshey had been with the Clippers for nine years, including stints as director of player development, assistant coach, director of player personnel and assistant GM. he was elevated to run the Clippers' front office in March 2010 after serving under Mike Dunleavy as the club's assistant general manager.
During Olshey's two seasons as the top executive in basketball operations, the Clippers improved from 29-53 in 2009-10, to 32-50 in 2010-11, then vaulted into the postseason this past season with a 40-26 record, the best winning percentage in franchise history.
He finished third last month in voting for the NBA's Executive of the Year for the 2011-2012 season.
"He has the skills and the vision to successfully guide our organization into a new era of Trail Blazers basketball," owner Paul Allen said in a statement released by the Blazers. "He's proven that he can quickly turn around a franchise, and we are confident he can do that in Portland."
Now that the Blazers have a general manager they can turn their attention to hiring a new head coach. The team dismissed Nate McMillan at the trade deadline after more than six seasons at the helm. Assistant Kaleb Canales served as coach the rest of the season.
The Blazers finished the lockout-shortened season 28-38 and out of the playoffs for the first time in four years.
And it was a campaign fraught with turmoil. Portland learned at the opening of training camp that three-time All-Star Brandon Roy was retiring because of ongoing issues with both knees. They also found out that center Greg Oden, the No. 1 pick of the 2007 draft, had suffered yet another setback with his surgically repaired knees. Portland would later waive Oden after he played in only 82 games in nearly five seasons.
Portland again enters an offseason in rebuilding mode, with four picks -- including No. 6 and No. 11 -- in the June draft. The team also has up to $24 million in cap space to work with on the free agent market.
Buchanan has said the priorities are re-signing French forward Nicolas Batum, and bringing in a quality point guard and big man.
p>Meanwhile, the Clippers exercised their option last week on coach Vinny Del Negro, bringing him back for a third season.
The Clippers are searching for a replacement for Olshey, whose responsibilities will be absorbed by Roeser, Del Negro and director of player personnel Gary Sacks.
The Clippers, in addition to a GM search, also face a summer of big decisions with star forward Blake Griffin eligible for a contract extension and Paul entering the final year of his contract.
But one source close to the process told ESPN.com's Marc Stein that Olshey's departure would have "no significant impact" on Griffin's decision, despite the fact that it was Olshey whose moves put the Clippers in position to trade for Paul in December when the Hornets' original three-team trade to send Paul to the Lakers was canceled by NBA commissioner David Stern, who was acting as the Hornets' lead decision-maker because the team was still under league ownership.
The Clippers, sources say, continue to believe that Griffin will accept an extension this summer as opposed to playing out the 2012-13 season and becoming a restricted free agent in July 2013.
Information from ESPN.com's Kevin Arnovitz and Marc Stein and The Associated Press was used in this report.