These orders, for 351 buses and 28 coaches, will also help Alexander Dennis's aim of continuing its strong growth in recent years under chief executive Colin Robertson.
Alexander Dennis, one of Scotland's major manufacturing businesses, was rescued from administration in 2004 by a consortium including Stagecoach co-founders Sir Brian Souter and Ann Gloag, Sir Angus Grossart's Edinburgh-based Noble Grossart merchant bank, and metals-to-property entrepreneur and former Rangers owner Sir David Murray.
Bill Simpson, group corporate affairs director of Alexander Dennis, said yesterday that it had hiked its turnover by about 35% to nearly £500m during 2012.
Mr Simpson noted this 2012 sales figure was nearly three times the turnover of about £170m achieved in its 2006 financial year.
Alexander Dennis's operating profits are likely to have grown significantly in 2012, from about £18.5m in 2011.
Mr Simpson highlighted Alexander Dennis's aim of achieving sales of more than £500m in 2013, and its expectation that half of this targeted turnover would come from exports as it continued its international expansion. He said the company had ended 2012 with a 50% share of the UK bus market.
He cited major moves by Alexander Dennis last year in the bus markets of North America, Australia, New Zealand, Hong Kong, China and Malaysia.
Mr Simpson said the latest order from Perth-based bus and rail group Stagecoach would not lead to the creation of new posts, but highlighted its beneficial impact on job security for existing staff.
Referring to the new business from Stagecoach, and citing orders for more than 600 buses from Hong Kong, which were announced in November, Mr Simpson said: "It is great news in terms of keeping everyone in a job and growing the business further."
Mr Simpson added that the bus orders won from Stagecoach included 245 "complete vehicles", with Alexander Dennis's chassis and bus bodies. The other 106 buses will have Alexander Dennis bodies and Scania chassis.
Alexander Dennis's Plaxton business in Scarborough, Yorkshire will build the bodies for 28 coaches, which will have Volvo chassis.
Stagecoach's corporate communications director, Steven Stewart, noted its "conscious decision" to keep investing in its fleet over the past few years even though the economy had been "really tough". He said, over the last six years, it had invested more than £445m in buses and coaches for the UK.
Mr Stewart emphasised the part this investment had played in Stagecoach's success in continuing to attract people out of their cars and on to buses and coaches. He said the bus and coach orders involved a competitive tender process, and noted neither Sir Brian nor Ms Gloag participated in deciding or negotiating any of the transactions with Alexander Dennis.
Stagecoach yesterday announced an overall investment exceeding £75m in a total of more than 430 new buses and coaches, which also includes orders for Optare and Belgian company Van Hool. While Stagecoach did not break out Alexander Dennis's share of this £75m-plus, it is understood to be about two-thirds of the total investment.
Mr Robertson, who joined Alexander Dennis in 2007, has a significant holding in the company. Of Alexander Dennis's total 2300-strong workforce, about 1900 employees are in the UK.