Shulkin also directed an assistant to plan day excursions for him and his wife, the IG said.
Health Secretary Tom Price resigned last September after an uproar over his use of private charter planes for government business.
Shulkin was a holdover from the Obama administration, where he served as an undersecretary in the VA, but his work at the VA has been highly touted by Trump.
Shulkin disputed the report's conclusions, but he said in a statement he would consult with counsel about whether he should pay for those items. "It is a direct assault on my spouse, my character and my unblemished record of service to veterans".
The inspector general's report recommends that Shulkin reimburse the department for the unnecessary travel costs, and reimburse an overseas acquaintance for the cost of the Wimbledon tickets.
"Even after you provided us with a copy of your draft report, your office's tactics seem intentionally created to prevent a full airing of the facts and circumstances underlying the trip", Shulkin's legal team wrote in a blistering 16 page letter, which was attached to the Inspector General report.
Prior to the trip, Vivieca Wright Simpson, Shulkin's chief of staff and the third highest-ranking VA official, "made false statements and altered a document" to create a pretext for taxpayers to cover the cost of airfare for the secretary's wife.
In fact, the OIG referred the incident to the Department of Justice to consider it for potential criminal prosecution, but DOJ declined to prosecute.
Missal said that Simpson took Gough's response and altered it to make it look like he had written, 'We're having a special recognition dinner at the US Ambassador's Residence in the honor of SECVA'.
Shulkin, along with his wife, senior VA leaders and a six-member security detail took the 11-day trip in July to meet with Danish veterans' healthcare officials and a VA summit in London. Airfare for Shulkin's wife cost more than $4,300, and costs for the entire trip topped $122,000. The trip included a tour of Westminster Abbey, attendance at the women's final at Wimbledon featuring American Venus Williams and a cruise on the Thames River.
He said the department usually has weeks to review and respond to reports, but he had only two working days. Acceptance of the tickets may have been prohibited by federal ethics rules.
The inspector general began a review in October after The Washington Post reported that Shulkin and his wife had spent almost half their time on personal activities during the European trip. The report "cast the VA, the secretary and others identified in the report in the least favorable light", Bowman said. The report says Shulkin asked for and received the tickets from Victoria Gosling, an executive with the 2016 Invictus Games, a sporting competition for wounded vets.
Shulkin, 58, took office as the 9th Veterans Affairs secretary exactly one year ago Wednesday. Shulkin's lawyers said Gosling was not a "prohibited source" because Gosling does not do business or seek to do business with the VA.
Mike Coffmans wants the head of the Department of Veterans Affairs to resign after a report revealed his office improperly accepted gifts and then mislead investigators.
That news came just days after Environmental Protection Agency head Scott Pruitt was found to have taken a number of expensive flights, including a first-class flight between NY and Washington, D.C. and a $7,000 business-class trip to Milan. Perry also has defended his travel as preapproved.
Pruitt's defense for his expensive travel is that flying coach has yielded "interaction that's not been the best". Treasury Secretary Steve Mnuchin and his wife have been targets of investigation - along with mockery - over their actions and excessive trips.