The 27 year old Scottish international defender has been a target of Martinez for a while and has chosen a move to the DW Stadium ahead of that of Middlesbrough.
The North East club have added three other Celtic players to their squad as Gordon Strachan raids his former club. However Caldwell has chosen a move to the top flight of English football.
The defender has been in contract talks with Celtic for a number of months now and it seems he has decided to take his football elsewhere. A £1 million fee is enough for Celtic to part with one of their star assets who is fast approaching the end of his contract.
He is expected to sign a two and a half year contract today and should be revealed to the press later this afternoon.
Caldwell has 36 Scotland caps and was named the Scottish Writers’ Player of the Year for his performances last season. He has played in Scotland for five and a half seasons since his release from Newcastle United in 2004.
He leaves Parkhead having won two Scottish Premier League winners medals, as well as a Scottish Cup and Scottish League Cup title. Caldwell has been an important part of Tony Mowbray's defence so far this campaign.