West Yorkshire Police said Thomas Mair, 52, has been charged with the murder of the 41-year-old, BBC wrote.
She was fatally injured outside her constituency surgery in Birstall, West Yorkshire, on Thursday, according to the report.
Mair will appear at Westminster Magistrates' Court later and faces a number of other charges, including grievous bodily harm.
He is further charged with possession of a firearm with intent and possession of an offensive weapon, the force said, according to BBC.
Prime Minister David Cameron said the whole nation was "rightly shocked" at her death and called for people to "value, and see as precious, the democracy we have on these islands".
Politics is about public service and MPs want to "make the world a better place", he said, BBC wrote.
