The song fuses rap with country music and is inspired by Avicii’s crossover hit Wake Me Up.
It is both Pitbull and Kesha’s third UK number one.
The Official Charts Company said Timber significantly outperformed what is traditionally one of the quietest weeks of the year for singles sales, with over 139,000 copies sold this week.
The news comes a few days after Kesha, 26, announced that she had checked herself into rehab to treat an eating disorder.
Last week’s chart topper, Pharrell Williams’s Happy, dropped to number two despite recording sales of 108,000 in the past seven days.
The top five was completed by Avicii’s Hey Brother and Jason Derulo’s Trumpets – both non-movers at three and four – while Ellie Goulding’s Children In Need single, How Long Will I Love You, climbed two places to five.
Singer-songwriter Goulding h celebrated a second number one album. Halcyon took 65 weeks to finally reach the chart summit.
Originally released in October 2012, the record features top 40 singles Anything Could Happen, Figure 8, Explosions, How Long Will I Love You and her first ever UK number one, Burn.
Gary Barlow held on to the number two spot with Since I Saw You Last, while Beyonce climbed one place to number three with her self-titled album.