Aldridge has taken 76 wickets in first-class cricket and scored more than 1,000 runs, with a best of 101 not out.
He was also part of the Somerset side that won the T20 Blast in 2023.
He played eight T20 games for Durham earlier this summer, which included personal-best bowling figures of 5-29 against Nottinghamshire Outlaws.
Durham’s director of cricket Marcus North said:, external “At only 24, Kasey has already established great foundations in all formats of his game, and we look forward to nurturing this very exciting talent in his next stage of his career at Durham.”