Open Britain, which officially launches later this week, will not call for a second referendum but will make the case for continuing to work closely with the EU and the benefits of immigration.
The organisation has developed out of Britain Stronger in Europe, the failed official Remain campaign from this year’s referendum on EU membership.
Mr Clegg, the former deputy prime minister, has been joined by politicians from both Labour and the Conservatives in backing Open Britain.
In a joint article, Conservative Anna Soubry, Labour’s Pat McFadden and Liberal Democrat Norman Lamb called for a balanced response to concerns about immigration raised in the referendum campaign.
They said: “June 23 was a moment of change. The strength of feeling is clear. Free movement of people cannot continue as it has done. It has to be reformed.
“This was not an expression of prejudice but rather a desire for managed migration and concern that rapid immigration can put pressure on public services and local communities.
“Britain must be open to talent, but with more ability to act if excessive competition in labour markets hurts our economy.”
Writing in The Sunday Times, they added: “Calls for reform must sit with a positive argument about the benefits that immigration brings.
“If we interpret the referendum result as a vote for a more insular and less inclusive country, or one in which the only way to advance working people’s living standards is to turn our face against the world, we will have converted a defeat into a tragedy.”
Open Britain is the latest group to emerge from the fallout of the June referendum.
Leave.EU, the organisation backed by millionaire Arron Banks which campaigned in the referendum in addition to the official Vote Leave group, has continued its operations arguing it will maintain the pressure on those negotiating Britain’s exit from the EU.
Remain supporters have also launched Vote Leave Watch to hold Leave supporters to promises they made during the referendum campaign.
Open Britain will be launched on Friday.