The pair will take over from Roger Herridge, who is stepping down from the role as Sumas drop into Hellenic Division One East and move back to Lowther Road.
Bateman is Herridge's current assistant and has worked alongside him since their days with the Sumas Allied Counties team.
Last week, Herridge told the News that Bateman would be the perfect man to take over as manager and he will now get his chance, along with former player Eggleston.
"I couldn't have achieved what I have without him," said Herridge. "He has got all the qualities to be a good manager. He is good with players, people and knows his football."