The 38-year-old veteran, playing for Durham, achieved the landmark by bowling out Hampshire for 115 in their first innings, finishing with figures of 10-47 off 17.3 overs.
Durham had made 252 in their first innings of the match being played at Chester-le-Street.
Gibson, who becomes the 79th bowler in first-class cricket history to achieve the feat, is the first since Debasish Mohanty in 2000-01, and first in county cricket since Richard Johnson took 10 for 45 for Middlesex in 1994.
He reached the mark when he bowled James Bruce for a first-ball duck.
"I'm as pleased as punch, it was my day today. I knew I had to bowl well early on and everything just clicked into place," said Gibson who is playing for his third English county.
"It was definitely one of my more disciplined act and it's nice to put in a performance that lifts the team."
However, Gibson, who payed two Tests and 15 one-day internationals, said he was too experienced to get carried away by his achievement.
"This was a great day, but it doesn't mean I should play for four more years. I've been around long enough to know that next week I might not take any wickets, so I still won't look much further than tomorrow.
"In my young days I was quick and I still like to bowl fast and rough people up when I have the chance, but in conditions like this I know it's best just to run in and let the ball do the work. I got the wickets more through swing than seam.
"I wasn't going to bowl after lunch, but the captain said I wasn't going to get many more chances to take all 10 at my age.
"It couldn't have worked out better for me because both times I started to feel tired I got a break, first for lunch then with the rain."