Mrs Cox had started work on the cross-party campaign before she was killed in her constituency last year.
The commission, in her memory, will work with 13 charities including Age UK and Action for Children to come up with ideas for change.
They will provide findings as part of monthly campaigns on people such as new mums, carers and the elderly.
'Sociable but lonely' - how it feels when loneliness strikes
The campaigners will put together a manifesto of the charities' findings and ask the government to look into ways of reducing the problem.
Research by the partners shows over nine million people say they are "always or often lonely", but two-thirds of those would not talk about it in public.
MPs want the report to be a call to action to encourage people to chat and start conversations. The commission is asking people to do more, for example knocking on a door or picking up a phone.
Mrs Cox's sister, Kim Leadbeater, said she wanted to continue the MP's legacy "by ridding society of loneliness one conversation at a time."
Mrs Cox, who was the Labour MP for Batley and Spen, suffered from loneliness when she went to university and was split up from her sister.
"It was one of those issues where she felt she could make a real difference," she told the BBC News Channel.
"I can't go back to normality because there is no normality without Jo, but what I can do is try and work to continue the good stuff that she did and try and make her proud."
Despite the family's "dark days", Ms Leadbeater said she would not be beaten by what had happened and that she would "come out fighting".
"I'm going to try and make some of the change and difference Jo can't make for herself anymore", she added.
The co-chairwoman of the campaign, Conservative MP Seema Kennedy, said loneliness could be "profoundly detrimental" on mental and physical health.
"If you are chronically lonely, it is as bad as smoking 15 cigarettes a day. You might have an increased risk of high blood pressure."
Mrs Cox was determined to shine a spotlight on how loneliness affects people of ages, Ms Kennedy said.
Colleagues and family members of the murdered Labour MP Jo Cox have launched a campaign to tackle loneliness.