A source told ESPN NFL Insider Adam Schefter that Finnegan signed a two-year contract.
Finnegan, who has no agent, represented himself in contract talks. The former St. Louis Rams cornerback said he spoke with a lot of general managers and coaches around the NFL, but his only free-agent visit was to Miami.
"It was a great experience," he said. "If I was like four years in the league, it would be cool to have an agent. The older you (are), you can understand where your market value is."
The Dolphins also signed another ex-Ram, guard Shelley Smith. He agreed to a $5.5 million, two-year deal, with $1.5 million guaranteed, then left town headed for his wedding.
Smith started eight games over the past two seasons for the Rams, including two last year.
Finnegan, 30, is projected to start opposite Pro Bowl cornerback Brent Grimes. The Dolphins also signed free agent safety Louis Delmas to a one-year contract last week in the effort to remake their secondary.
Finnegan was recently cut by the Rams after playing in just seven games in 2013 due to a hamstring injury and then an eye injury that required surgery.
"You can never know how much a guy has left in the tank if he's injured," Finnegan said. "I was injured most of the year. Now it's a clean slate. I'm on a new team with great coaches, and I've got to let my play do the talking."
Finnegan recorded 27 tackles and one interception last season. The Dolphins were looking for a veteran to add to the mix with their young cornerbacks, who include 2013 draft picks Jamar Taylor and Will Davis.
General manager Dennis Hickey said the Dolphins like Finnegan's zeal on the field.
"He has been a tough playmaker over his career, with a veteran presence and leadership and love and passion for the game," Hickey said.
The Dolphins have been active during the first week of free agency. In addition to Finnegan, Smith and Delmas, Miami signed left tackle Branden Albert.
The Associated Press contributed to this report.