The remarkably swift deal, which both of them have signed, was concluded just 11 days after Holmes filed for divorce and followed marathon negotiations between two teams of lawyers over the weekend.

Cruise is thought to have been especially keen to avoid a drawn-out court case that could have highlighted details about him and Scientology. The constroversial church has repeatedly been cited as a reason for the couple’s separation and it has faced a torrent of bad publicity in the past fortnight.

It is understood their six-year-old daughter Suri will live primarily with Holmes, but that Cruise will have generous visitation rights and be a full part of the child’s life.

Holmes, who was raised a Catholic, is thought to have secured her wish that Suri not be brought up in the Church of Scientology.

On one visit to her lawyers’ offices in New York at the weekend Holmes spent six hours discussing the deal, which also includes a property settlement.

Holmes is currently living in a three-bedroom apartment in New York with Suri, while Cruise is based primarily in Los Angeles with his two adopted children Connor, 17, and Bella, 19.

In a joint statement the couple said: “We are committed to working together as parents to accomplish what is in our daughter Suri’s best interests.

“We want to keep matters affecting our family private, and express our respect for each other’s commitment to each of our respective beliefs, and support each other’s roles as parents.”

The reference to “respective beliefs” appeared to confirm that Scientology, and its role in Suri’s upbringing, was a key factor in the split.

Holmes filed for divorce on June 28 and Cruise was said to have been stunned. She also filed for sole custody of Suri with a court in New York.

There had been suggestions Cruise would apply to have the case transferred to California where he would have a better chance of custody.

But, according to aides, he was said to be reluctant to “drag his family though the mud” and wanted a private settlement.

Aides indicated that he would never accept being cut out of the child’s life completely, but would approve a deal if he was given “meaningful and significant” access to Suri.

That appears to have been achieved to Cruise’s satisfaction. The actor, who is on location filming in the Rocky Mountains, has not seen his daughter since the divorce papers were filed but has spoken to her daily by telephone.

Holmes’ lawyer Jonathan Wolfe said: “The case has been settled and the agreement has been signed. We are thrilled for Katie and her family and are excited to watch as she embarks on the next chapter of her life.

“We thank Tom’s counsel for their professionalism and diligence that helped bring about this speedy resolution.”

Cruise, 50, is Hollywood’s highest earning star, having made $75 million (£48 million) in the last year, but the financial settlement is not expected to feature in lists of the most costly divorces.

Holmes, 33, signed a cast iron prenuptial agreement before the marriage five years ago, and has indicated she wants to “earn her own money” from her acting career.

Bert Fields, Cruise’s lawyer, told celebrity website TMZ: “Tom is really pleased we got there, and so am I.”