"It's all happened incredibly quickly, but I am delighted to be here," Fletcher said in a statement.
"This is a fantastic club with a top manager and a great group of players and I am really looking forward to this opportunity.
Fletcher won four Premier League titles, an FA Cup and 2008 Champions League with Manchester United before joining West Brom on a free transfer in February 2015.
The 33-year-old scored six goals in 97 appearances for West Brom and was handed captaincy by manager Tony Pulis shortly after his arrival at the Hawthorns.
(Reporting by Hardik Vyas in Bengaluru, editing by Pritha Sarkar)
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