The deal is reportedly worth $23.8 million over four seasons due to the NBA's rookie wage scale. Ingram, a forward, was the last of the 60 draft choices to sign his contract.
Ingram starred at Duke in his lone college season. He averaged 17.3 points and 6.8 rebounds and knocked down 41 percent of his 3-point attempts.
He played himself into the second selection behind LSU forward Ben Simmons, who went first overall to the Philadelphia 76ers.
Ingram is the latest building block for the Lakers, who drafted guard D'Angelo Russell last year and forward Julius Randle two seasons ago. Los Angeles also has a new coach in former Golden State Warriors assistant Luke Walton.
The Lakers posted a franchise-worst 17-65 record last season.