Zakuani, who was appointed Spalding United manager earlier this week, has continue his signing spree, including the recent signing of former Premier League striker Nile Ranger.
Assombalonga, 30, a striker, has previously featured with Dagenham and Redbridge and Billericay Town.
Bolasie lists North Greenford and Aylsebury Vale Dynamo among his former sides.
On Foster, a centre-back, Zakuani said: “Jordan is a player I’ve always had my eye on and I’ve had to work hard to get him on board.
“He’s a big strong lad who will give us the physicality I feel we’ve been lacking. I’m looking forward to working with him”
Foster added: “I’m grateful for the chance to play for Spalding United.
“I’m excited to be around seasoned professionals that make up the coaching team, and can’t wait to get started.
“This is the right move for me, I feel this is a great place for me to continue learning and developing.”