Bayern Munich forward Toni Kroos left the door open for a switch to the Barclays Premier League in the summer.
Tim Sherwood claims the "silence is deafening" from the Tottenham board amid speculation he could be replaced as manager.
Town boss Mick McCarthy revealed over the weekend that the defender was set to pen a move to Portman Road and the terms of the agreement have now been signed and sealed.
After putting pen to paper, Brown told the club's official website: "This is a big challenge for me and I'm excited to be signing for Ipswich. It's a big club with great facilities and I'm looking forward to meeting all the lads and getting started.
"I've played here once before, in an Under-15 Academy showcase game for United, so it's nice to be back here again and I'm ready to try and prove myself at Ipswich.
"I'm still only 21 years old and getting experience at a Championship club like Ipswich is good for me and it's all part of my education."
Brown, younger brother of Sunderland defender Wes, is yet to make his first-team debut for United but has enjoyed 29 appearances during loan spells with Bradford, Doncaster, Oldham and Coventry.