Sapp, a sixth-round pick by the Ravens in 2003, is expected to compete for the starting free safety job as well as provide an impact on special teams.
The Ravens waived Sapp after the 2004 season opener, a move not fully endorsed by the entire organization. Sapp later said the Ravens intended to cut cornerback Corey Fuller, but Fuller talked the coaches out of it by reminding them how he got Deion Sanders to sign with the team.
Sapp has since become a solid special teams performer for the Colts while Fuller played sparingly the rest of the 2004 season, his last in the NFL.
The trade with Indianapolis is contingent on Sapp passing a physical.
"We looked at it as an opportunity to upgrade our football team," Ravens general manager Ozzie Newsome said of the trade.
Sapp has the most playing experience in the battle for the free safety spot even though he has just two starts (both coming in the Colts' last two meaningless regular-season games last year). He will compete against Dawan Landry (a fifth-round pick), B.J. Ward, Jamaine Winborne and Robb Butler.
"We take everybody to camp and play the best 11," Newsome said.
In 16 games last season, Sapp made 28 tackles on special teams and 16 on defense.
A restricted free agent, he signed a one-year tender worth $721,600. He will be an unrestricted free agent at the end of the season.
It marked the Ravens' second player trade with the Colts, who relocated from Baltimore in 1984. The Ravens sent a third- and fourth-round pick to Indianapolis in 1998 for quarterback Jim Harbaugh and the Colts' fourth-round selection.