The Colombian won by just two seconds, salvaging his yellow jersey in the final stage after Spaniard Contador (Trek Segafredo) pulled away 50km from the finish.
Contador picked up two seconds in time bonuses at the intermediate sprint and another six by taking second place in the eighth stage behind compatriot David De La Cruz (Quick Step Floors).
Henao, who started the day with a 31-second advantage over Contador, crossed the line 21 seconds after his rival.
"I'm happy with my performance. It was not easy because everybody knew that I would attack. However, it was a beautiful day of cycling," Contador told reporters.Last year, Team Sky's Geraint Thomas beat Contador by four seconds to win Paris-Nice.
Sky have come under fire for failing to prove what was in a medical package ordered by a team doctor and delivered to Bradley Wiggins at the 2011 Criterium du Dauphine.
Team Sky and British Cycling have both been subject of an investigation by UK Anti-Doping (UKAD) into allegations of wrongdoing in the sport. Both have denied any doping violations.
"I dedicate this victory to the team, the staff... I am proud to be part of this team," Henao told reporters.
BEAUTIFUL LOSER
Contador, who says he'd rather be remembered as a beautiful loser than an ugly winner, was true to his swashbuckling style, launching a long-range attack in the penultimate climb of the day.
Henao was quickly dropped and Contador's lead grew past the minute.
But in the final descent and on the flat ride to the finish in Nice, Henao received help from some Bahrein-Merida riders as he managed to reduce the gap.
Contador was beaten in a two-man sprint by De La Cruz, which cost him four seconds in time bonuses, and eventually the overall win.
"I panicked a little bit at first, but then I just thought I had to ride like in a time trial," said Henao.
"We were all thinking about what happened last year when Geraint won. I was confident but obviously it was a close call."
It was a sweet victory for Henao, who had been voluntarily withdrawn from racing by Sky for three months in March 2014 after their own monitoring of his blood values and his out-of-competition tests showed some irregularities during his winter training block at high altitude in Colombia.
He was withdrawn again in 2016 after concerns re-surfaced about his biological data before being cleared by the UCI.
Asked about the affair on Sunday, Henao said he had "no problem making his file public".
(Reporting by Julien Pretot, editing by Pritha Sarkar)
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