The singer will perform 20 shows under the banner Lionel Richie - All the Hits through April and May, and September and October next year.
The cheapest tickets, which go on sale on Friday, start at $59 (Â£38).
Richie, 66, said the decision was made to perform after consulting his 21-year-old son, Miles.
"I asked him, 'so Miles, what do you think about Vegas? Should I do it?'," said Richie.
"He goes, 'Oh my God, dad. We are going to have the great time. We are going to have the greatest time."
The singer played the traditional Sunday afternoon legends slot on the Pyramid Stage at Glastonbury in June.
His 80-minute performance is regarded by many as one of the highlights of the weekend.
His Vegas shows will include hits such as All Night Long (All Night), Hello and Dancing on the Ceiling.
Richie is also to be honoured by The Recording Academy as its MusiCares person of the year.
Previous recipients include Sting, Bono and Aretha Franklin.
Performers at the event on 13 February include Pharrell Williams, Luke Bryan and Lady Antebellum.
"I think Stevie (Wonder) is coming maybe," said Richie. "But first of all, let me tell you, what a great honour.
"When you're in that group of honourees. When you start thinking about Dylan and Streisand and stuff ... that's quite an accomplishment."

The two probationary officers, aged 23 and 24, appeared before Assistant Chief Constable Robin Smith, who recommended they should be dismissed.
Both officers have since resigned, Sussex Police said.
The investigation came after they filmed themselves near the site of the air crash where 11 people died after a jet crashed on to the A27 on 22 August.
The recording was made at the police cordon and accompanied by an inappropriate and offensive message.
Sussex Police launched an internal investigation after the footage and message were sent on social media to a colleague who reported the pair.
The force said both constables exercised their right to tender resignations under regulation 13, a provision specific to probationary officers.
Chief Constable Giles York said the pair were "clearly remorseful" and had acknowledged the impact of their actions, but would not go on to become "well-conducted officers" in his view.
"When it really mattered the officers failed to show understanding and compassion for the victims and their families," Mr York said.
Genuine mistakes were forgivable, he added, but said the behaviour of the two officers was "inexplicable and caused unnecessary distress to the families of those involved".
The Sussex Police Federation, which had represented the two officers throughout the case, said: "We are content that they have been judged fairly and accept and understand the decision that has been reached."

The 23-year-old mutually cancelled his deal at the Shrimps earlier this month but can train at the Championship side ahead of the move.
"Agreeing the pre-contract deal now, I get the opportunity to bed myself in before I can play again," he said.
"I think this will be a really good challenge for me."
Morecambe boss Jim Bentley had spoken about selling a player to raise funds for the Lancashire side who paid their players late at the start of November.
Despite cancelling Barkhuizen's contract at the Lancashire club, they retained his rights so Preston had to pay the compensation package.
Find all the latest football transfers on our dedicated page.
Following his barnstorming set at Glastonbury, soul legend Lionel Richie has announced a residency at the Planet Hollywood Resort & Casino in Las Vegas.
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Two Sussex police constables questioned over their conduct at the site of the Shoreham air crash have left the force.
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Preston North End have signed forward Tom Barkhuizen from League Two side Morecambe for a compensation fee with the deal to go through on 1 January.