You are now in possesion of a written offer that you want to accept.
To progress things you now need to resign verbally and then confirm your resignation in writing. Good practice is to confirm your resignation in writing to your line manager but to copy your personnel manager.
A sample resignation letter is as follows
Dear X
Thank you for your time at our meeting today where I verbally resigned my position. I am now confirming my resignation with immediate effect.
As required by my contract of employment I am giving the company X months notice and as such my final date with the company will be X.
I look forward to the company settling all outstanding salary, commission , expenses and pro-rata holiday entitlement in due course.
In closing I would like to thank you for your support during my employment and want to take this opportunity to wish both you personally and the company every success for the future
Yours sincerely
This letter is succinct clear , unambiguous and is all that you need to say in writing.