The 26-year-old Bury racer headed into the largely processional final stage into Madrid with a one minute and 46 seconds lead and avoided any late mishaps to land his first Grand Tour title.
The three titles had never before been held by three riders from the same country.
Yates said: “It’s astonishing really. Growing up I was so accustomed to seeing the French, Italian and Spanish riders lead the way, so for myself, Chris and Geraint to all win a Grand Tour in the same year just shows how far the sport has come in this country.”
Froome, whose Tour-Vuelta double in 2017 meant British riders had at that point won five Grand Tours in a row, paid tribute to Yates’ achievement, saying: “Simon has looked so strong over the last three weeks and it’s great to see him take home the maillot rojo. It’s been a perfect year for British riders.”