The ‘Braveheart’ actor – who has six sons and one daughter with ex-wife Robyn and a daughter with ex-girlfriend Oksana Grigorieva – welcomed his grandson, whose mother is Mel’s daughter Hannah, on Saturday night.
A source told People: “He was overwhelmed with emotion. He gets that way around babies. He was overjoyed.”
Following the birth, Mel spent Sunday morning at a church in Malibu before heading to see the newborn, who is yet to be named.
The 55-year-old star also spent part of the weekend with his 17-month-old daughter Lucia, his child with Oksana.
The source added: “He always has a great time with her.”
Last week, Mel was sentenced to a year-long domestic counselling programme after pleading no contest in a Los Angeles court to a charge of misdemeanour battery against the Russian singer.
The pair remain embroiled in a custody battle over Lucia, and his former lover is also planning to file a civil case against Mel alleging battery, emotional distress and defamation.
In addition to counselling, Mel also must carry out 16 hours of community service with Mending Kids International, an organisation that provides surgical care to disadvantaged children worldwide.