Best was drafted into the squad after Northampton captain Dylan Hartley received an 11-week ban for verbally abusing referee Wayne Barnes in the Aviva Premiership final.
The Lions will not officially decide on Hartley's participation on the tour until the result of any potential appeal is known - but he was absent from Sunday's official farewell dinner at the Royal Courts of Justice.
Best, who had been due to captain Ireland on their summer tour, will now link up with the Lions as one of three hookers, along with Tom Youngs and Richard Hibbard, heading out to Hong Kong.
Head coach Gatland said: "When we picked the squad it was very, very tough. The decision on the hookers was by far the longest debate we had.
"Rory was very, very unlucky to miss out. One man's disappointment is another man's fortune and I am sure he will come in and do a great job. In previous tours, when players have had that chance they have come in and made the most of it. He has the chance to do that."
Hartley was sent off just before half-time in Leicester's 37-17 victory and banned after being found guilty of calling referee Barnes a "f****** cheat".
Alan Quinlan, who suffered depression after a ban for eye-gouging cost him a chance to go on the 2009 Lions tour, tweeted: "I do feel sorry for Dylan Hartley. It's a tough time for him now. Go easy on him."
For Best, the news was the perfect tonic after Ulster's RaboDirect PRO12 final defeat by Leinster and he is now determined to live up to the challenge Gatland has set him.
"It was hard when I didn't make the initial squad because it is everyone's ambition. To now be selected is a massive honour," he told ulsterrugby.com. "To finally be selected makes playing professional rugby worthwhile. All the lows that you get and the knocks and bumps, it more than makes up for them and for a few weeks ago when I thought that the chance had gone."
- Sports & Recreation
- Dylan Hartley
- Wayne Barnes
- Tom Youngs