René Angélil, 72, was previously diagnosed with throat cancer in 1999, when his wife took time off her career as he recovered.
A statement released by René's publicist on Friday revealed that the operation took place on 23 December and was a success.
It also stated that Celine's husband and manager had spent a few days in hospital before beginning his recovery at home in Las Vegas.
Celine, 45, said in the statement that she wants her husband to focus on getting healthy and to avoid the daily stress of work.
"I want him to focus on getting back to 100 per cent," she said. “I’ve been doing my shows at the Colosseum and everything's under control.
"At home we’ve been spending a lot of quality time with the family. We feel very fortunate that we’ve been able to get the best care possible and we thank God every day for helping us to get through this ordeal."
The Canadian songstress has been married to her hubby for almost two decades. The couple, who share a 26-year age gap, went on their first date when Celine was 19 and René was 45.
By 1991, the couple got engaged and were eventually married in 1994, at the Notre-Dame Basilica in Montreal, Quebec.
They have three children, 13-year-old René-Charles and twin boys Nelson and Eddy, who were born in 2011, following her sixth attempt at IVF.
"They're so cute, it's incredible," said Celine in an exclusive interview with HELLO! magazine at the time. "When we look at them we can't believe it, and to have them here at home – it’s all we could wish for."
The boys, who were born when Celine was 35 weeks pregnant, were in a neonatal intensive unit for several days before returning to their home in Florida.