Known for his overpowering fastball, fiery temperament and bushy mustache, the Goose received 466 of 543 votes (85.8 percent) from 10-year members of the Baseball Writers' Association of America.
"It was very emotional, off the charts. I can't describe the feeling," Gossage said.
Jim Rice was passed over yet again, getting 392 votes (72.2 percent), up from 346 (63.5 percent) last year but 16 short of the 75 percent needed. He will appear on the writers' ballot for the 15th and final time next year, when career steals leader Rickey Henderson will be among the newcomers.
Andre Dawson was third at 358 (65.9 percent), followed by Bert Blyleven at 336 (61.9 percent), Lee Smith at 235 (43.3 percent) and Jack Morris at 233 (42.9 percent).
Mark McGwire, a casualty of the Steroids Era in some writers' minds, received just 128 votes -- the exact total he had last year. His percentage increased slightly to 23.6 percent, up from 23.5 percent last year when he was on the ballot for the first time.
Tim Raines topped the 11 newcomers on the ballot, receiving 132 votes (24.3 percent). All of the others appearing for the first time fell below the 5 percent necessary to remain on the ballot next year.
Gossage, who fell short by 21 votes last year, joins Hoyt Wilhelm (1985), Rollie Fingers (1992), Dennis Eckersley (2004) and Bruce Sutter (2006) in Cooperstown's bullpen.
Gossage was sitting in a recliner in his living room overlooking the Rocky Mountains when he received the call. He turned to reporters in the room and said, "Oh my god, I've been elected."
"A shock wave went through my body like an anvil just fell on my head," Gossage said about his reaction. "I think having to wait makes it that much more special."
His mother died in 2006, Gossage said with tears welling up in his eyes, and he had hoped she would live long enough to see him inducted.
Gossage was a nine-time All-Star who pitched for nine major league teams from 1972-94 and had 310 saves -- 52 of them when he got seven outs or more.
The first time he appeared on the Hall ballot in 2000, Gossage received only 33.3 percent of the vote.
He will be inducted July 27 in Cooperstown, joined by five men elected last month by the revamped Veterans Committee: former commissioner Bowie Kuhn, former Dodgers owner Walter O'Malley, managers Dick Williams and Billy Southworth and ex-Pirates owner Barney Dreyfuss.
Williams managed Gossage on the San Diego Padres.
"There isn't anybody I'd rather go in with than Dick Williams," said Gossage, who spoke with his former manager right after getting the news.