Keen spent nine years on the coaching staff at Upton Park and was named caretaker manager on three occasions, most recently for the final game of last season, a 3-0 defeat at home to Sunderland.
He will work alongside Steve Clarke - also a first-team coach - at Anfield having signed a three-year deal, and will report with his new colleagues for the first day of pre-season training on Monday.
Dalglish said: "I'm delighted that Kevin is joining us to work alongside Steve Clarke coaching the first team squad.
"He has previously worked with Steve at West Ham and has a good reputation and a good manner about him. He is highly respected in the game and will be a great addition to our technical staff."
Keen made over 600 appearances in spells with West Ham, Wolves, Stoke, Macclesfield and Wycombe.