Collins departs the club having made 214 appearances during two spells in East London, while Evra only arrived on a short-term deal in February.
Reports emerged last week suggesting that Collins had been told via email by West Ham that his contract would not be renewed for a further year, causing anger among the fanbase.
While the circumstances surrounding the ex-Wales international's exit remain unknown, the Premier League side have announced that neither he nor Evra will be retained.
"His bravery and commitment on the pitch were never called into question and he has played his part in establishing the club in the Premier League since his return in 2012.
"We appreciate just how popular James is among our fellow supporters but, with the appointment of a new manager, we felt together that the time was right to go our separate ways. It goes without saying that we wish James and his family every success in the future and they will always be welcome at London Stadium."