Bush, who was Florida's governor from 1999-2007, formally joined ranks with the Republican nominee at a Republican Party unity rally in Jacksonville after supporting Attorney General Bill McCollum in last week's primary.
Bush said he has no reservations about getting behind Scott's self-funded candidacy.
"He has the practical experience from the private sector to execute on his dreams, and your dreams will come true with Rick Scott as your next governor," Bush said. "I hope you spend all the time you can to elect this good man."
Bush earlier this summer described Scott's outsider campaign as "weird," but he said Tuesday that he's been impressed with the nominee.
"It's more than appropriate to look at the general election and say this is the guy to lead us," Bush said. "I was for Bill McCollum ... he's a good friend, but I wasn't against Rick Scott."
Scott talked with Bush about a lieutenant governor selection, but neither would divulge the names they discussed.
"I'll have a running mate everybody will be proud of," said Scott, who will announce his choice Thursday. "This person is going to do a wonderful job."
The Duval County Republican headquarters building was surrounded by Scott campaign signs and the 200 or so who squeezed inside wore Scott campaign buttons — though many conceded they had backed McCollum's failed bid for the nomination.
Bush said he was hopeful that McCollum would soon get over his defeat and endorse the nominee.
"I've been there," Bush said, referring to his 1994 defeat by Gov. Lawton Chiles in the closest gubernatorial race in Florida history. "It hurts."
Scott is running against Democrat Alex Sink, the state's chief financial officer, and independent Lawton "Bud" Chiles III, the son of the late Democratic governor.
Chiles, however, has indicated in recent days that he's thinking about dropping out of the contest.
Sink's campaign announced Tuesday that 10 Republican elected officials — mayors, city commissioners and council members from across Florida — have endorsed her.
The Jacksonville rally was the second of the day staged by Republican leaders seeking to assure voters the party stands united behind Scott.
Mississippi Gov. Haley Barbour, head of the Republican Governors Association, joined Scott and about 200 mostly elderly supporters at a Miami-area community center.
Scott's campaign called the appearances a "unity tour," a week after a terse exchange between Scott and the governors' group over a primary ad attacking McCollum.
Senate President Jeff Atwater and incoming House Speaker Dean Cannon emphasized Republican teamwork was needed to send Scott to the governor's mansion in November instead of members of what they called " Obama's team."
"He won a great victory in a tough primary. Now I'm tickled to see all these legislators here to support him," Barbour told the crowd.
When reporters asked Scott about intraparty squabbles before the primary, he responded with criticism of President Barack Obama's health care law and the federal deficit.
"It's great to have (the governors association's) support to make sure that our agenda of building jobs is the winning agenda," Scott said.
Barbour pledged that the association would spend millions to help Scott's campaign.
Before the Aug. 24 primary, the Republican Governors Association had asked Scott to pull an ad tying McCollum to indicted former state party chairman Jim Greer. Scott refused, saying Barbour's request was an example of "Washington insiders" rallying for McCollum.
The day after Scott won the primary, the group urged all Florida Republicans to back Scott. On Tuesday, Barbour downplayed the dustup, saying the factual inaccuracy in the ad was no longer an issue.
"That's water under the bridge," Barbour told reporters.