The signing was first reported by ESPN NFL Insider Adam Schefter.
Three-time league MVP Peyton Manning hopes Baskett can find his way around the offense fast.
"Hopefully we can catch him up as soon as possible," Manning said. "It's a lot of offense to learn in a couple of days but he's a veteran, so he could help us."
The Colts play Miami on Monday night.
The Colts have been in the market for a receiver since losing Anthony Gonzalez to a knee injury.
But Gonzalez sprained ligaments in his right knee Sunday and is expected to miss several weeks. Colts coach Jim Caldwell said Thursday that Gonzalez could miss up to eight weeks.
The Indianapolis Star, citing a source, reported Thursday that Gonzalez won't require surgery.
Baskett was one of seven receivers the Eagles carried on their 53-man roster through Week 1. He became expendable after Philadelphia selected Jeremy Maclin in the first round of April's draft and added Brandon Gibson in the sixth round.
Baskett had 72 catches for 1,052 yards and six touchdowns in 48 games with the Eagles.
Information from The Associated Press was used in this report.