The final stage, a 144km route from Hawit Nagam Park to the Matrah Corniche on the coast of Muscat, ended as predicted in a bunch sprint.
Froome held a 27-second advantage over Alberto Contador, with Cadel Evans a further 12 seconds adrift going into the last day.
And by finishing safely in the bunch the Team Sky rider held on to complete the first stage-race victory of his career.
"It wasn’t just a straightforward finish, it had a little bit of a climb on the final circuit which made it a test right down to the last couple of kilometres," Froome said afterwards.
Team Sky Sports Director Nicolas Portal explained his team's approach to the race.
"The good thing about this race was that we achieved exactly what we wanted to do, which was to return to the Sky style of racing," he said. "To control from the front and, when we commit to something, to really commit to it and carry it out together as a team. All the things we were doing last year.
"Without the radios it is not easy sometimes so the guys did really well. We have taken a stage win and the GC so that bodes well for the future. We did lots of great work in Mallorca and now we can see how well that has translated into the races."
Nacer Bouhanni of FDJ won the stage, pipping Matthew Goss and Taylor Phinney to the line.
Gatis Smukulis of Katusha was the first to make a breakaway, while a couple of chasers, Wesley Kreder and Andrea Di Corrado then joined him. They stretched their lead out to 6:30 at one stage, but that began to dwindle as the racers approached the final circuit in Muscat.
With two-and-half-laps - about 15km - of Muscat to conclude the Tour, the breakaway group were pulled in and a sprint became an inevitability.
Team Sky held control of the peloton in the final stages, overseeing Froome's ride to the line. Philippe Gilbert of BMC briefly ascended to the front, but in the end both were left behind.