Rotherham-born custodian Flinders, 29, has agreed a one-year contract with the option of a second season after turning down a new deal at Ronnie Moore’s Hartlepool United.
The 6ft 4in ex-England U20 keeper started his career with Barnsley in 2005 before a big money move to Crystal Palace a year later.
After making only 11 appearances for the Eagles during his three-year contract at Selhurst Park and taking in a number of loan spells away from the London club, he was released in May 2009.
Flinders subsequently joined Hartlepool and has been a regular for the past six years and could ironically make his home league debut for the Minstermen against Pools at Bootham Crescent on August 15.
Pools are now being linked with a move for released Hull City veteran Steve Harper.
Meanwhile, Halifax-born Berrett has completed his move to York from Yeovil Town.
The former Huddersfield and Carlisle midfielder has signed a two-year deal after being allowed to leave Huish Park following the Glovers’ relegation to League Two last season.
The arrival of the duo follows on from the earlier capture of former Wolves defender Geroge Swan - son of ex-York, Hull and Leeds player Peter - and ex-Crewe forward Vadaine Oliver.