The Northern Ireland international has signed a two-year contract at Tannadice where he will compete with Benjamin Siegrist, who has been linked with a summer move.
The 33-year-old helped Motherwell to two cup finals and established himself as his country's number one but has had a frustrating time since suffering deep vein thrombosis on his return from international duty in November 2018.
Carson did not play again until August 2020 after losing his Motherwell place to Mark Gillespie, and missed most of last season with a knee injury. He has moved on after Motherwell signed Liam Kelly from QPR.
The former Hartlepool keeper told United's website: "There was talk of me moving back down to England for family reasons, but once Dundee United came in for me and I spoke to the gaffer and sporting director Tony Asghar it was a no-brainer to come here.
"It's such a great club with a great history, I'm so excited to be part of it.
"Benji was one of the top goalkeepers in the league last season so I know it's going to be a challenge for me. You've got to embrace that, I've been in the game a long time and if you're not up for a challenge then you're in the wrong sport.
"One of my short-term goals is to come and give Benji a good run for his money. Hopefully, it will be a healthy competition."
United head coach Tam Courts added: "Trevor is an experienced international player who has performed well in the Scottish Premiership and has built a strong reputation for his performance levels.
"He joins a motivated goalkeeping group who push each other every day, so he's a welcome addition to what we're aiming to do."
A Motherwell statement read: "We wish Trevor all the best for the future, and thank him for all he did for our club."