He told his followers: ‘To my truest love… out of nowhere, you made 45 hands down the greatest year of my life. And i’m sure it took me 45 years to become the man worthy of your love.
‘I hope I spend every one of these birthdays by your side til my last day. And beyond. Forever and ever yours (and yes, we got married).’
The pair are said to have got engaged earlier this year and made their first public appearance together in July at an event hosted by Gucci in the Hamptons, New York.
It was reported in August that the pair were planning their wedding but had had to cut their guestlist down due to the coronavirus pandemic.
Grace is an actress, following in the footsteps of her mother, and has starred in American Horror Story, Mr Robot and The Newsroom among others.
She was previously married to musician Tay Strathairn, the son of actor David Strathairn, but the couple separated after just 42 days of marriage in 2019 and their divorce was finalised last year.
Mark married French model and actress Josephine de La Baume in 2011 after she appeared in the music video for his track The Bike Song the previous year, but they split in 2017 and were divorced in 2018.
He was also previously engaged to The Office star Rashida Jones in 2003 but the pair parted ways a year later.
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