These services were previously provided by iGo buses.
Nick Vane, Commercial Director of National Express Coventry, said:
"We are pleased to announce that from Monday 1st April, National Express Coventry has taken over the operation of the 539 to Kenilworth, and the 580 to Rugby - a town that we have not served before and which we are delighted to be able to include in our expanding network.
"We have worked hard to mobilise these services at short notice to ensure that local communities do not lose their vital bus connections to key destinations."
The timetables remain the same, with National Express Coventry day tickets and travelcards valid on all services. Copies of the timetables are available online here.