Thorp is currently head of government affairs and comms for Europe and Canada at the firm, having held various other roles previously including senior director, corporate affairs and market access for Lilly UK.
At National Grid, he will report to group corporate affairs director George Mayhew.
Prior to Lilly, Thorp worked for Novartis and GSK, and served in the Royal Navy, according to LinkedIn.
His team includes head of media relations Sean Kemp, a former Downing Street comms spad, who joined from an agency role last year.
The National Grid, in addition to operating the UK's electricity and gas infrastructure, has large distribution and power generation operations in the US. The group had revenues of £15.1bn in the year to 31 March. Of its 25,000 staff, 15,000 were based in the US.