Mr Sharon was admitted to hospital after suffering a stroke on Sunday evening while being driven from his official residence in Jerusalem to his ranch in the southern Negev desert, raising doubts about his long-term future ahead of a March 28 general election.
But he told reporters he was in a rush to return to work as he left the Hadassah hospital and then phoned Netanyahu to congratulate him on being elected leader of the premier's former Likud party.
"I must hurry to return to work so that we can move forwards," said a weary-looking but smiling Mr Sharon in a play on words on the name of his new Kadima party, which means "forwards" in Hebrew.
His office said Mr Sharon had contacted Mr Netanyahu "to congratulate him on winning yesterday's Likud primaries and to thank him for his get-well wishes."
Weekly check-up
Despite giving Mr Sharon a generally clean bill of health, doctors said they still needed to keep an eye on him.
Mr Sharon would have to return for a weekly check-up and had been recommended to take anticoagulant drugs to prevent any repetition of the clotting that led to his stroke, said professor Shlomo Moryussef, a director of the hospital.
Mr Sharon, known for his voracious appetite, also received advice from US President George W Bush who urged him to adopt a healthier diet.
"Begin to do some exercise, eat healthily, with no fat, and sleep well," Mr Bush was reported to have told Mr Sharon in a phone call.
The latest batch of opinion polls showed that the premier's health scare has not frightened voters off supporting his new Kadima party but they made grim reading for Mr Netanyahu after his election as head of Mr Sharon's old Likud party.
Mr Sharon's hospitalisation added a dramatic backdrop to voting yesterday for a successor as leader of the party which he quit a month ago in order to establish Kadima.
After seven other cabinet ministers jumped ship with Mr Sharon, Likud has been left with a right-wing rump who unsurprisingly chose Netanyahu to rebuild their electoral fortunes.
Mr Sharon's decision to leave Likud was made after he grew fed up with battling hardliners such as Netanyahu who refused to forgive him for pulling Jewish settlers out of the Gaza Strip.
Polls favour Kadima
A month ago, Likud was the largest party in the 120-seat Knesset with 40 MPs, but the large scale defections have raised the prospect of an electoral meltdown when the country goes to the polls on March 28.
A survey for Israel’s daily Maariv newspaper forecast Kadima would win 42 seats, against 22 for the centre-left Labour party while Likud should win just 13.
Mr Netanyahu however was in bullish mood after being formally declared winner in the early hours, pledging to lead Likud back to power.
"I came here tonight to tell you that as of now, the Likud is beginning the march back to reclaim the leadership of the country," he told supporters at Likud's Tel Aviv headquarters after his main challenger, Foreign Minister Silvan Shalom, conceded defeat.