The Sale player, who can also play second-row, excelled in a weak Scottish pack during this year's Six Nations.
And the hard-tackling 27-year-old was considered unlucky by many to miss out on a place in the original squad.
Jason, who has 46 international caps, is expected to arrive in New Zealand on Wednesday ahead of Saturday's second Test in Wellington.
Jason had expressed his disappointment at not being called up following Lawrence Dallaglio's departure from the tour.
The fact he still had his broken thumb in a cast probably counted against him and Ireland's Simon Easterby was given the nod instead.
And when Wales' Ryan Jones was drafted in following an injury to Scotland's Simon Taylor it looked as though White's Lions dream was over.
Jason said to www.scottishrugby.org: "Obviously I'm absolutely delighted to be going out to join the tour. Time's quite tight to be getting involved with the games but I'll be giving it 100% and do whatever I can to help achieve success and contribute to the matches. Having the familiar faces of Chris [Cusiter], Gordy [Bulloch], Gavin Scott and the medics [Dr James Robson, Stuart Barton and Bob Stewart] should help me settle in and I'm really looking forward to it."