The former City keeper, a free agent after failing to agree a new deal at Cardiff has signed a three year deal at Portman Rd.
Also today former City defender Rhys Weston has completed a move to League 1 side Walsall.
Alexander said of his move,
"I'm delighted to have joined Ipswich Town and am looking forward to the next step in my career.
"The club has a fantastic tradition in the game and, talking to the manager, it's clear that he has a great desire to take Ipswich Town back to the Premiership."
Meanwhile Weston has penned a one year contract in the West Midlands,
'I'm really excited by the move and I'm looking forward to the challenge ahead," said the Welsh defender.
'It's been an interesting journey up until this point and I'm looking forward to the next stage in my career.'