In addition to Tulowitzki, the Rockies sent 42-year-old reliever LaTroy Hawkins to the Blue Jays.
Along with Reyes, the Rockies picked up reliever Miguel Castro and two minor league pitchers.
Fox Sports first reported the teams had agreed to a trade involving Tulowitzki, Reyes and minor leaguers.
Tulowitzki, 30, is owed $113.7 million through 2020, according to MLB.com, and would receive a $2 million bonus for being traded.
His contract also would convert to include a full no-trade clause from here on out, per Fox Sports.
A source told ESPN.com's Jayson Stark there is "zero chance" the Blue Jays turn around and flip Tulowitzki to another team.
Tulowitzki was in the manager's office in the visitors clubhouse after the Rockies' 9-8 walk-off loss to the Chicago Cubs on Monday night, according to ESPNChicago.com's Jesse Rogers. At some point, Colorado manager Walt Weiss walked in as well.
Members of the media waited around in the locker room but were eventually made to leave and told by the Rockies' public relations staff that the trade was not official.
Tulowitzki was not made available for comment.
"I can't announce anything. Nothing is official," Weiss told reporters. "There's a lot of things going on right now. It's not official so there is nothing to announce."
Prior to the game, Weiss was asked whether he had talked to Tulowitzki about handling distractions arising from trade rumors ahead of Friday's 4 p.m. ET trade deadline.
"I've talked to these guys as a group about all the distractions that come with the trade deadline," Weiss said. "Basically, I told them to control what they can control. There are always distractions at this level during this time period."
Tulowitzki was at the center of trade talks in May but said at the time that he was not looking to leave the Rockies.
"Whatever happens on the Rockies' end happens, but for me to sit here and try to force my way out of here, that's not the case," Tulowitzki told reporters in May, according to MLB.com. "I don't think it's fair to my teammates and the relationships I've built here to take that route."
Tulowitzki has spent his entire nine-year career in Colorado after he was drafted seventh overall in 2005.
The Gold Glove-winning infielder is a five-time All-Star and was considered an early front-runner for the 2014 National League MVP award after a hot start that saw him post a line of .421/.522/.794 (BA/OBP/SLG) with seven home runs and 22 RBIs in the first month of the season.
He injured his left hip during a July 20 game, however, and underwent labral repair surgery in August that forced him to miss the rest of the 2014 season.
Tulowitzki is batting .300/.348/.471 with 12 home runs and 53 RBIs over 87 games in 2015. He is a career .299 hitter.
Hawkins saved just two games this season before losing his job as the Rockies' closer. But in his past 14 appearances, he has posted a 0.68 ERA in 13⅓ innings. In that span, he has struck out 11, walked one and yielded seven base hits.
Toronto would be the 11th team Hawkins has played for in his career, three more than any other active player. He previously said he would retire after this season.
The Rockies currently are in last place in the NL West at 42-55.
The Blue Jays, meanwhile, are hoping to make a late-season run at the New York Yankees in the American League East. Toronto currently trails New York by seven games. The Blue Jays have the longest active playoff drought in baseball, with their last appearance in 1993, when they won the World Series
Reyes heads to Colorado after a 2½-year stint in Toronto, during which the Blue Jays failed to make the postseason despite lofty expectations.
He was sidelined early this season with a fractured left rib suffered on a check swing in the fourth game of Toronto's 2015 campaign.
The four-time All-Star and 2011 NL batting champion is batting .285 this year with four home runs, 34 RBIs and 16 stolen bases in 69 games.
The 32-year-old shortstop then joined Toronto in the offseason after just one season in Miami.
In February 2014, he told MLB.com that it "means a lot" to him that the Jays weren't quick to jettison him after an injury-marred 2013 season in which Toronto fell far short of expectations.
The Jays also bid farewell to Castro, a 20-year-old reliever who struggled after taking over for Brett Cecil as the team's closer in April and was demoted to Triple-A in May. He has a 10.13 ERA with two losses and two blown saves over his past seven appearances.
Information from The Associated Press and ESPN Stats & Information was used in this report.