A source told LOOK magazine: "I think it's something Tom's been thinking about a lot recently, but especially as July was approaching. It's like he's finally recognised that Katie will always be the love of his life.
"It was such a shock when she left him - although she would no doubt argue that he ignored the signs - terms with that decision but I think Tom finally understand why she had to end things.
"It's taken a long time for him to come to and let go of the anger, but it seems like he finally has and he obviously will have wanted to tell her that."
The former couple - who reportedly only communicate via intermediaries - are said to have attempted to call a truce in March, but have barely exchanged words since. Thrice-divorced Tom is now more determined than ever to rekindle his friendship with Katie for the sake of their seven-year-old daughter Suri - who he sees regularly.
Discussing the difficulty of arranging visitation plans for Tom to see Suri, the source added: "Tom obviously desperately wants that to change. I'm sure, as well as telling her how he feels.
"That'll have been a huge motivation behind the letter. It's about getting their relationship on better terms."