EXCLUSIVE

They TRIED to make it work ... but Arian Foster's wife has decided to pull the plug on their marriage ... more than a year after the NFL star fathered a child with another woman.

TMZ Sports has confirmed the Houston Texans star's wife, Romina Lombardo Foster, filed for divorce in Texas on April 22 ... seeking to end their 4 year marriage.

Romina tells us, "After much thought and soul searching, I have made the difficult decision to end our marriage."

Arian says the two are ending the relationship on extremely good terms -- saying the marriage "has been nothing but a gift."

"I’m extremely grateful for the wife, mother and person she was to myself and our children. I will continue to be here and support her wholeheartedly on her next journey as I’m sure she’ll do the same for me."

As we previously reported, Foster fathered a child with another woman last year. He and Romina tried to repair their relationship, but in the end, Romina decided it was best to move on. They have two young children together.

Here are statements from Arian and Romina in full ...

Statement from Arian:

"After 4 years of marriage, it has been nothing but a gift. I’m extremely grateful for the wife, mother and person she was to myself and our children. I will continue to be here and support her wholeheartedly on her next journey as I’m sure she’ll do the same for me. We have two beautiful children that are the center and focal point for both of our lives and I’m forever thankful that we crossed paths. At this time please respect the privacy of her, myself and most importantly our children."

Statement from Romina:

"After much thought and soul searching, I have made the difficult decision to end our marriage.