The striker will undergo a medical on Wednesday before officially signing for the Reds.
Crouch deal done
"He's had Liverpool after him and many players would have thrown their dummies out of the pram but he's come in every day, worked hard and been a fantastic example to everybody," said Southampton boss Harry Redknapp.
"This is the second time I've sold him - I sold him at Portsmouth for £5 million, so maybe I'll meet him again and sell him again.
"I wish him well and I'm sure he'll be a big success at Liverpool."