Davis, the 25th overall selection in the 2009 draft, made 132 tackles and nine interceptions during his three seasons in Miami.
The Colts, under new general manager Ryan Grigson and first-year head coach Chuck Pagano, have embarked on an aggressive overhaul of their roster.
They have sent their second-round choice in the 2013 draft and a conditional late-round pick to the Dolphins in exchange for Davis.
"Bottom line with this move today [Monday] is we got better as a football team," said Grigson on the team's official website.
"That is always the goal each day for this organisation. From the first time he stepped on the field at Illinois as a freshman or in the National Football League as a rookie, you knew Vontae was a special talent.
"Now he has a chance under Coach Pagano and this coaching staff to reach not only his potential as a football player, but as a person as well. That is our collective goal moving forward."