It’s late night with … Stephen Colbert!

The comedian will replace David Letterman on the “Late Show” when the longtime host retires next year, CBS announced on Thursday.

Colbert, who now hosts “The Colbert Report” on Comedy Central, signed a five-year deal to take over the show, saying he “never dreamed” he’d have the honor.

“Simply being a guest on David Letterman’s show has been a highlight of my career. I never dreamed that I would follow in his footsteps, though everyone in late night follows Dave’s lead … I’m thrilled and grateful that CBS chose me,” Colbert said.

He joked, “Now, if you’ll excuse me, I have to go grind a gap in my front teeth.”

Colbert will retire his signature character, a faux-conservative talking head, and will work on “The Colbert Report” for eight more months.

CBS has not yet revealed whether the “Late Show” will be shot at its current home at the Ed Sullivan Theater, which is located on Broadway between 53rd and 54th.

But since he’s already based in New York City, it’s likely Colbert — and the “Late Show” — will remain in Manhattan.

CBS Chairman and CEO Les Moonves is thrilled the satirical funny man will take over, he said.

“Stephen Colbert is one of the most inventive and respected forces on television,” Moonves said.

“David Letterman’s legacy and accomplishments are an incredible source of pride for all of us here, and today’s announcement speaks to our commitment of upholding what he established for CBS in late night,” he added.

Letterman himself also praised Colbert as the right man for the job.

“Stephen has always been a real friend to me. I’m very excited for him, and I’m flattered that CBS chose him. I also happen to know they wanted another guy with glasses,” Letterman said.

It remains to be seen how the news will impact Craig Ferguson, who hosts the “Late Late Show,” which follows “Late Show” at 12:35 a.m.

Ferguson’s contract with CBS automatically gives Letterman’s empty chair to Ferguson if he wants it, while awarding him $5 million if he is passed over.

There’s also no word on how Comedy Central will fill the hole left when Colbert leaves “The Colbert Report,” the show he’s hosted since 2005

“Comedy Central is proud that the incredibly talented Stephen Colbert has been part of our family for nearly two decades,” the network said in a statement.

“We look forward to the next eight months of the ground-breaking ‘Colbert Report’ and wish Stephen the very best.”

Letterman announced his retirement on April 5 after a record-setting 21 years on the show.

Fans and showbiz types took to Twitter to cheer the choice on Thursday.

“Nobody on television right now is more talented than Stephen Colbert. CBS is lucky to have him” tweeted @julieklausner.

Comedian Kristen Schaal gushed, “@StephenAtHome! You will be the best at the desk! But I will deeply miss the Colbert Report.”

The airing date and location of the show will be announced “at a later date,” CBS said.