Hello.
There are usually two parts to this.
Part 1 is removing your name from the mortgage itself. The lender will normally agree to this provided your former partner can afford this. This varies from lender to lender but usually this will be a maximum of about 4 - 5 times his salary but they will be less if he has credit cards, loans, hire purchase and/or any other loans. Also, take into account any loans secured on the home. Hopefully if the mortgage is less than 75% of the current value of your home, the lender may be a bit less strict on the need for your former partner's income to fit the criteria I mentioned already.
Secondly, your name has to be removed from the property itself. A good solicitor can do this for you and provided both of you are cooperative it can be done fairly quickly.
The first part usually goes through quicker than the second simply because a former partner can waste time to be vindictive but I don't think that this will necessarily be the case in your situation because you are both in the same home and seem to be getting on.
Total costs will be in the lower hundreds and should not take longer than a month.
I wish you success.