The pair have been reunited at Palace having previously worked together at Stoke City, Portsmouth and Plymouth Argyle.
Kemp's appointment as the Eagles' new technical coach sees him return to the club where he spent three seasons as a player between 1974 and 1977, playing 44 times and scoring 16 goals.
Pulis said: "David has a wealth of experience in the Premier League and will be a fantastic addition to the coaching team here at Crystal Palace Football Club.
"We've worked together for many years and have the same philosophy on tactics and work ethic. I know the staff and players at Palace will enjoy working with David and he will join us on the bench at Spurs tomorrow."