The couple asked the famous artist - whose previous works have included a shark pickled in formaldehyde - to create a painting of a lilac heart to hang in one-year-old Harper's bedroom.
Asked his most recent extravagance, David - who also has sons Brooklyn, 13, Romeo, nine, and Cruz, seven, with Victoria - revealed: ''A piece of artwork which I had specially made by a friend.
''We named it 'Daddy's Girl'. Who was the artist? Damien Hirst.''
After raising three sons, David is still astonished that he now has a daughter too.
He said: ''I'm still amazed we have a little girl. I change her nappy and I'm still amazed that it's a girl. Amazing.''
Because they are so busy with the kids, the 37-year-old soccer star and his fashion designer wife always make time for regular date nights but he is adamant their ''main priority'' is always their children.
He added in an interview with Esquire magazine: ''As much as we work hard and we love to spend time with our kids, and that's our main priority, we make sure we go out for dinner once a week.
''But our number one priority is our kids. Nothing work-wise, relationship-wise ever comes between that. We do what we have to do. We both work really hard. But One Of Us is always with the kids. If I'm away, she's here, if she's away, I'm here.''