Tate has joined up with his new team-mates and will be in the Glovers squad for their friendly at Exeter on Tuesday night.
The 30-year-old started his career at Manchester United and joined the Swans in 2004 following a series of loan spells.
Tate has represented Swansea in all four divisions of English football, making more than 300 appearances.
He returned from a broken leg last year and was sent out on loan to Leeds from November until January.
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