Britney Spears has nothing but praise for her ex, Sam Asghari, in her memoir ... calling him a "gift from God" despite a rocky split, and it's a clear sign they've either settled their divorce or they're super close.

In the singer's new book, she recalls being "instantly smitten" by the actor/model when they first met on set in 2016 -- calling him an "inspiration, adding she instantly knew "I wanted him in my life."

Brit says the chemistry between them was insane ... "We couldn't keep our hands off each other." She says he was her rock during the contentious conservatorship hearings ... crediting him for giving her the courage to speak out.

What's interesting ... there's no talk about their acrimonious divorce at all. We know Britney made changes to her book after Sam filed for divorce back in August, so she could have changed her tune, but she didn't.

As we reported, their relationship was extremely volatile, at times she became physical with him and screaming matches were common. Yet none of it is referenced in the memoir.

Sam also praised Britney and her book recently, so when you put it all together, it seems like they've struck some kind of a divorce deal that satisfies both of them.