The agreement, which values the division at $271.4 million (£214.4m), comes just weeks after the bus and rail giant revealed that talks were underway to off-load the North American arm.
An £85.4m writedown in the division had sent the group reversing into the red at the half-year stage.
The sale to private equity firm Variant Equity Advisors will see the Scots group receive $207m and transfer net debt of $64.4m. The deal is expected to complete by the end of the group’s financial year to 27 April.
Stagecoach’s US business includes megabus.com inter-city coach services, commuter services, airport transportation, sightseeing tours and charter services. But it has been struggling amid increased competition.
The group said the disposal would allow it to “realise an attractive valuation” for the business while refocusing its UK division and concentrating on growth opportunities in its domestic market.
Chief executive Martin Griffiths said: “During our two decades in the North American transportation market, our success included reinvigorating the inter-city coach sector and delivering growth with our innovative megabus.com brand.
“We have a great team of people who have ensured we have played a leading role in the development of public transportation in the United States and Canada.
“The sale of our North American operations will allow management to focus more closely on the significant opportunities for growth in the UK.
“We have strong bus and rail operations in the UK where public transport has good prospects as the clear solution to the challenges of increasing road congestion and poor air quality.”
The group’s US business employs some 4,500 people and operates a fleet of more than 2,000 buses and coaches.
In the six months to 27 October, the division saw revenues fall 3.2 per cent, while earnings fell to $21.2m from $27.6m.
Gerald Khoo, a transport analyst at brokerage Liberum, noted: “The group needed to get big or get out. Given the headwinds to demand from lower fuel prices making car travel and airline competitors more price competitive, growing megabus organically was challenging.”
“Against that backdrop, exiting North America appears the better option, in our view, despite the slightly disappointing valuation achieved.”
Interim results released earlier this month by Stagecoach, covering the six months to 27 October, revealed that the group swung to a pre-tax loss of £22.6m compared with profits of £96.7m a year earlier.
The interim dividend was maintained at 3.8p.