It is understood that Jarvis chairman Paris Moayedi met Network Rail chief executive John Armitt last Monday to inform him.
Jarvis chief executive Kevin Hyde said the main reason was that the contracts prepared by Network Rail would have meant more risk and lower margins.
Network Rail said rival contractors were queuing to take over the work.
Jarvis is under investigation over the train crash at Potters Bar, Hertfordshire on 10 May last year in which seven people were killed.
It has apologised for the derailment of one train at King's Cross station last month.
Jarvis' decision led to a 16p jump in its share price, up to 323.5p.