In a trading update yesterday, the Perth-based group also declared that its overall profitability remained satisfactory, while reporting solid year-on-year growth in revenues in its UK rail business and in its bus operations on both sides of the Atlantic.
It noted the US Department of Justice and New York Attorney General had, as previously reported, initiated litigation against Twin America and its joint venture partners, which include two Stagecoach US subsidiaries, in 2012.
The litigation alleges that the formation of the Twin America joint venture in 2009 was anti-competitive. Separately, private plaintiffs brought a claim based on the same allegations on behalf of a proposed class of customers.
Stagecoach revealed that the defendants, Twin America and its joint venture partners, had not admitted any liability but had agreed a cash settlement of $19 million (£11m) with the private plaintiffs to fully resolve the private litigation.
It said: "That settlement will be submitted to the court for preliminary approval. Assuming the court grants its preliminary approval, final court approval is anticipated in approximately nine to 12 months following a period for class notification and claims administration."
Stagecoach added: "The government action remains pending at this time. Until the government action concludes, the total financial cost of the various actions cannot be determined. The allocation and funding of any financial settlements among the various defendants is currently being discussed."
The company said it currently anticipated recording exceptional pre-tax costs of around $15m (£9m) in the year to April 30 in respect of its share of financial costs connected with the litigation.
It added: "The ultimate cost to the group may differ from this as it remains dependent on the outcome of the government action."
Stagecoach reported that revenues in its UK bus business, outside London, were in the 48 weeks to March 30 up 4.8% on the same period of the previous financial year on a like-for-like basis.
It said that revenues in the 48 weeks to March 30 in its UK rail business, excluding its Virgin Rail joint venture on the West Coast Main Line, were up 4.5% year-on-year on a like-for-like basis. This UK rail division includes the South West Trains and East Midlands Trains franchises.
Stagecoach is waiting to find out whether or not its bids for the Docklands Light Railway and Thameslink franchises have succeeded.
Stagecoach said it continued to work on its bid with Sir Richard Branson's Virgin for the InterCity East Coast rail franchise, but now anticipated around £2m of the bid costs it previously expected to be incurred in the year to April 30, 2014 would be deferred until next year.
It reported revenues in its North American business, which includes the Megabus.com coach operation, were in the 11 months to March 31 up 4.1% on the same period of the prior financial year.
Stagecoach, chaired by Sir Brian Souter, said trading in its North American business had been satisfactory, in spite of prolonged adverse weather across the US.
It noted Virgin Rail continued to earn a fee equivalent to 1% of revenue from the West Coast franchise. It added that Virgin Rail and the Department for Transport were discussing revised commercial terms which could see Virgin Rail take greater revenue and cost risk for a period, from a date to be agreed through to April 2017, for a commensurate financial return.
Stagecoach said: "Although we face a number of challenges to growing profit in the year ending April 30, 2015, overall current trading is satisfactory and the prospects for the group remain positive."
Shares in Stagecoach rose 2.7p or 0.7% to 376.6p.