Tindall told the club in January that he wanted a two-year contract - but Gloucester were only prepared to offer a one-season extension and the talks went no further.
The 33-year-old is among a number of high profile players leaving Gloucester in the summer, including Rory Lawson, Alasdair Strokosch and Scott Lawson.
Gloucester took the decision to allow the Scotland international trio to leave because they are absent from club duty for the November internationals and two months over the RBS 6 Nations.
Number eight Luke Narraway is joining Strokosch in heading for Perpignan next season.
Eliota Fuimaono-Sapolu is bound for Japan while the likes of Tom Voyce and Brett Deacon are yet to find new clubs.
Before Bryan Redpath resigned as head coach, he oversaw the recruitment of New Zealand scrum-half Jimmy Cowan, England number eight Ben Morgan, Australian hooker Huia Edmonds, Tongan loose forward Sione Kalamfoni and England Saxons centre Billy Twelvetrees.
They will come in as direct replacements for Rory Lawson, Narraway, Scott Lawson, Strokosch and Tindall.
Gloucester will begin their process of identifying after their final Aviva Premiership game of the season, against London Irish.
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The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
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The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
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The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.