High-end fitness chain Equinox is launching one of the most expensive gym memberships in the world — a $40,000-per-year program aimed at improving overall health and longevity.

Equinox is teaming up with lab-test startup Function Health to launch “Optimize by Equinox,” a personalized health program that includes everything from personal training and nutrition plans to sleep coaching and massage therapy. The program, announced Monday, is part of the fast-growing market for longevity and…