WASHINGTON—Veterans Affairs Secretary David Shulkin improperly accepted a gift of Wimbledon tennis tickets, misspent taxpayer money and misused department resources in an official trip to Europe last year, according to an inspector general’s report released Wednesday.

The report also said a department employee acted as a “personal travel concierge” during the trip to Europe, and that Dr. Shulkin’s chief of staff made false claims to a VA ethics official by altering an email to get official approval for Dr. Shulkin’s wife to...