What a horrible thing to find out.
Firstly, please be gentle on yourself, this is a huge thing to process. A year’s affair is a secret life, a relationship with another woman, .
The first thing to establish is why did he tell you? Why exactly now? You talk about him regretting it, regret is nothing, you need to see remorse. Alleviating his guilt is still all about selfishness and entitlement, exactly what got him into the affair in the same place, same cheater thinking. If it was to give you your personal agency back, a chance for you to live a life away from someone who did this to you, then you’ve got a remorseful spouse.
Staying is of course possible but you have so much to unpick before you can even think about that. The minutiae of the affair, a timeline, all these things will become important to you. You’ll need to know how much he has done to work on being a safer partner for you.
I’d read ‘leave a cheater gain a life’ essential reading whether you stay or go to get into cheater mindset. Then I’d take a look at ‘how to help my spouse heal from my affair’ and get him to read it, to understand what remorse looks like and how to rebuild trust and help you feel safe again if that is what you want!
I’m so sorry.