"It was hard when I didn't make the initial squad because it is everyone's ambition to play for the Lions, but to be selected now is a massive honour," said Best.
"To be finally selected makes playing professional rugby worthwhile and makes up for the feeling I had a few weeks ago when I thought the chance had gone."
Meanwhile, Munster back row Peter O'Mahony has been made captain for Ireland's summer tour of North America in Best's absence.
The 23-year-old O'Mahony has impressed for Rob Penney's side this season and during the autumn internationals and the RBS 6 Nations, he made himself a mainstay of the Ireland back row.
He will be Ireland's youngest captain since Brian O'Driscoll led the men in green on their tour of Australia in 2002.