Please don't do this.
Has he been paying half the mortgage and half of all the bills and any home improvements for the past ten years, or has he just been 'chipping in' a bit less while you paid more because you own the house?
I doubt it.
If less, then where is all the money he saved by living with you that he should have been putting into his own home?
Is he going to put in an equal amount to the amount you have paid towards this house and is he expecting to only pay a half share of what you paid for the house, or does he expect a half share of the current increased value and does he intend to pay you some form of compensation for the loss of that profit on YOUR investment for the past decade?
Is he likely to run up debts?
If so, they can be attached to the house if his name is on the mortgage and his credit will be improved by being a home owner so he will have more chance to get into it.
Do you have someone you planned to leave your property to when you die?
If he is on the mortgage he gets at least half of it to leave to whoever he wants.
Are you considering moving in the future?
You will be handing him control over selling and may end up having to pay him to get your equity out?
When you wanted children, he didn't want to be a family with you, or care what you wanted.
When you wanted to jointly buy a house and it would have been equal, he didn't want to financially commit to you.
This isn't about you.
He's offering 'his hand' (which he thinks you want) as a bribe to gain your house so he has put a price on your relationship now he sees an advantage for himself to doing so.
This is about him wanting to be on the property ladder and gain an asset for under market value.