Lions coach Warren Gatland confirmed on Tuesday morning that 24-year-old Warburton will lead the Lions on their tour of Hong Kong and Australia this summer.
Bale knows Warburton well as they were in the same year at Whitchurch High School in Cardiff, and he is delighted that the Wales skipper has been given the prestigious honour.
"It's fantastic news for Sam," the Tottenham forward said.
"It's probably the ultimate accolade in rugby to be Lions captain and he deserves it.
"He's done fantastically well for Wales, captained them, won the Grand Slam, the Six Nations and he's still only young.
"This is another massive achievement and I'm sure he will take it all in his stride and end up being the best player out there."
Bale has enjoyed personal success of his own over the last 48 hours.
The 23-year-old, who is enjoying the best season of his career, won the PFA's Player of the Year and Young Player of the Year award at a glittering awards ceremony on Sunday evening.
Bale and Warburton's former PE teacher Glyn Morris spoke of his immense pride that the school had felt because of the duo's achievements.
Bale remembers Warburton being an all-round star during their time together at the Cardiff school.
He added: "Sam was always good at his school work, which I wasn't! He was great at every sport. He played football, rugby and athletics.
"He was an all-round sportsman and he's showed that in rugby. He's very quick compared to many players in his position. He's doing fantastically well and has a huge future in the game."