Lil Wayne now has official numbers to back up his bragging — the rapper’s new CD has sold a spectacular 1 million copies its first week.

“Tha Carter III” is easily the best selling first week of the year, according to Nielsen SoundScan figures. Even Kanye West’s “The Graduation” didn’t eclipse that mark in its first week last year (though it was only about 50,000 copies short).

A prolific rapper who’s been ubiquitous on the mixtape scene and on other acts’ records, Lil Wayne is generally regarded as one of rap’s most gifted performers — but he’s never had a multiplatinum album. His last two albums, “Tha Carter” and “Tha Carter II,” sold 1.1 million and 1.4 million copies, respectively. “Tha Carter III” was anticipated as the CD that would send the New Orleans rapper into superstardom.

“I’ve been saying a million all along, and I’ve been telling people, and they’ve been looking at me crazy,” said Ron Williams, co-founder of Lil Wayne’s record label, Cash Money Records.

“He worked hard. He just came with something different. He let his skills show on a lot of mixtapes. He’s featured on a lot of people’s records,” Williams said. “It just made people anticipate his record more than ever.”

Already, Lil Wayne’s had a No. 1 smash for several weeks — the sexually explicit “Lollipop” — and has been featured on numerous hits over the past year, including the recent remix to Usher’s “Love in This Club.”

In a slumping industry where selling 200,000 albums in one week is becoming a rare feat, Lil Wayne’s achievement is not only a triumph but a much-needed boost — the last CD to sell 1 million or more in its first week was 50 Cent’s “The Massacre” in 2005.

Expectations for “Tha Carter III” were high, and it delivered — selling 423,000 copies in its first day of release. It achieved blockbuster numbers despite being heavily bootlegged and leaked on the Internet; past leaks of material for the CD caused parent label Universal Motown to delay its release several times.

Lil Wayne, 25, has been a star on the rap scene since he was a teen, but only in recent years has his star rivaled that of contemporaries like West, a contributor on his new CD.