Mrs Cox, a mother-of-two and MP for Batley and Spen, was fatally attacked in Birstall, West Yorkshire, yesterday.
Lutonians who wish to pay their respects to the 41-year-old have been invited to attend a vigil outside Luton Town Hall on Monday at 5pm.
A book of condolence will be opened at the event and will be placed in the reception at Town Hall for those who wish to sign.
In a statement Luton Borough Council leader Hazel Simmons said: “On behalf of MPs Kelvin Hopkins and Gavin Shuker, the whole council, and people, faith and community organisations across Luton, we wish to express our utter heartbreak at the senseless killing yesterday afternoon of Jo Cox, MP for Batley and Spen.
“We share the devastation at the loss of a woman, a mother, a daughter and a wife, who entered public service to enrich the lives of people in her local area and much wider afield.”
Cllr Simmons added: “We send our sincerest and deepest condolences to her family, husband Brendan and two young children, and hope they can draw strength in the difficult times ahead from the positive difference Jo made to so many people’s lives.”
Earlier today Luton South MP Gavin Shuker paid tribute to Mrs Cox, who he said was an “incredible talent”.