The departures of Manchester United's Hargreaves and Tottenham Hotspur's Woodgate were both widely expected after injuries blighted their spells with their clubs.
Hargreaves' time at Old Trafford was cursed by physical problems and the combative midfielder made only 39 appearances after joining to considerable fanfare from Bayern Munich for £17 million in 2007.
Former Real Madrid defender Woodgate was similarly blighted and spent much of his three-and-a-half years at Tottenham on the treatment table.
The elegant defender was often touted as England's most naturally gifted centre-back but managed only four games in his final two seasons.
World Cup winner Vieira, who turns 35 next week, was released by Manchester City after playing a bit-part role in their resurgence since joining them from Inter Milan in January last year.
England international Matthew Upson was one of eight players released by West Ham United as the Premier League's relegated clubs looked to reduce their squad numbers.
Blackpool released 11 players as they prepare for their return to England's second tier, while Birmingham City shed 12 from their books including former England striker Kevin Phillips.
Another French World Cup winner Robert Pires was released by Aston Villa after joining on a free transfer in November and former Liverpool, Chelsea and Netherlands midfielder Boudewijn Zenden was let go by Sunderland.
