McGill’s is understood to have acquired First Scotland East, which operates in the Stirling, Falkirk and West Lothian areas.
The firm said they would be renamed as McGill’s Midland Bluebird and McGill’s Eastern Scottish, but collectively operate as McGill’s Scotland East.
McGill’s is believed to be taking over First’s depots in Livingston, Larbert, Bannockburn and Balfron.
The deal also includes Bright Bus Tours in Edinburgh, which First launched in 2019 to rival Lothian’s bus tours of the capital.
First confirmed the deal on Wednesday, which will involve the transfer of more than 200 buses and some 550 staff.
It described McGill’s as a “safe pair of hands”.
It sold its Borders operations to West Coast Motors’ offshoot Borders Buses in 2017, while its East Lothian services were saved by Lothian in 2016 after it threatened to close them down.
McGill’s, which operates in Inverclyde, Glasgow and Renfrewshire, took over Xplore Dundee, the city’s main operator, in 2020.
In an announcement to staff on Tuesday, First Bus Scotland managing director Duncan Cameron said: “First Bus has announced its intention to sell First Scotland East (FSE) to another Scottish operator, McGill’s.
"Under what is known as a share purchase agreement, all depots, routes and vehicles, including Bright Bus Tours, owned by FSE will transfer to McGill’s.
"All colleagues working for FSE will move to work for McGill’s and we expect this to be effective from September 19.
"There are no redundancies or job losses and this does not impact our Aberdeen or Glasgow colleagues or operations.”
Mr Cameron added on Wednesday: “This sale is part of a strategic refocusing of our Scotland business with significant investment in zero-emission buses in Glasgow and Aberdeen.
“As we’ve seen from their successful purchase of Xplore Dundee, McGill’s is an historic and trusted bus operator brand within Scotland and one we believe to be a safe pair of hands to take the Scotland East business forward successfully.”
McGill’s Bus Group chairman James Easdale said: “Our team are passionate about using our expertise to build the business in the years ahead so we can retain and attract new passengers across the region.”
Chief executive Ralph Roberts said it would “seek to deliver the best bus service possible.
"We firmly believe we can combine the advantages of the McGill’s Group with unique local transport brands.”