Former Manchester United striker Dwight Yorke is among seven players to be released by Sunderland.
Tal Ben Haim and Calum Davenport also leave having completed loan spells.
The Black Cats parted company with striker Djibril Cisse on Monday after deciding not to make his loan move from Marseille permanent.
The clean-out follows Sunderland's last-gasp Premier League survival on Sunday, despite a 3-2 home defeat by Chelsea.
The Wearsiders are pressing ahead with their search for a new manager and have seen new owner Ellis Short take complete control, in a busy week for the club.
Yorke, who turns 38 in November, made his final appearance last month against Manchester United.
Connolly, 32, has been plagued by injury and has not played since January 2008.
Former Barcelona 'B' team captain Riera was sent off just three minutes into his first start for the club in August 2006 and has not played since.
Wales international Darren Ward has also struggled for fitness, while Republic of Ireland international Nick Colgan failed to make an appearance for the first team.
Defender Peter Hartley has moved to his home town team of Hartlepool, while Davenport returns to West Ham and Ben Haim to Manchester City.