David Lancaster, 60, struck wife Helen, 54, six times with the weapon and smothered her with a pillow at their home in Tewkesbury, Gloucestershire.
The father of one took the sledgehammer from the garden shed before creeping upstairs, Bristol Crown Court was told.
Lancaster must serve at least 11 years and nine months in prison before he can be considered for parole.
Judge Neil Ford said a house owned by the couple in Lincoln - which was in Mrs Lancaster's name but had been bought by Lancaster with money he had inherited - was a source of "further annoyance and upset" for the defendant, who killed his teacher wife on 30 September.
The judge told him: "Your relationship had been in difficulty for some time.
"You suspected she had been having an affair with another man. On 20 August your suspicions were confirmed and you confronted Helen".
He added: "I have no doubt that you began to contemplate the benefit of killing your wife.
"Helen had revealed to friends that you had accused her of stealing your inheritance."
The judge told Lancaster: "You said you had been driven to commit murder by the way your wife had treated you and your daughter.
"You also said what you had done was less serious than what your wife had done to you and Amy.
"You have effectively deprived your daughter Amy of both her parents."
After the attack Lancaster fled the house, driving to a beach at Burnham-on-Sea in Somerset, where he was later arrested.
He rang the police and confessed to murdering his wife and told them where to find her body.
Lancaster pleaded guilty to murder at a previous hearing.
A man who murdered his wife with a sledgehammer because she was having an affair has been jailed for life.