They are: Chuka Umunna, Luciana Berger, Chris Leslie, Angela Smith, Mike Gapes, Gavin Shuker and Ann Coffey.
Ms Berger said Labour had become institutionally anti-Semitic and she was "embarrassed and ashamed" to stay.
Mr Corbyn said he was "disappointed" the MPs had felt unable to continue working for the policies that "inspired millions" at the 2017 election.
The MPs are not launching a new political party - they will sit in Parliament as the Independent Group.
But Chuka Umunna said they had "taken the first step" and urged other Labour MPs - and members of other parties - to join them in "building a new politics".
"Politics is broken, it doesn't have to be this way. Let's change it," he said at a launch event in central London.
He said there would be "no merger" with the Liberal Democrats and the group wanted to "build a new alternative".
Chris Leslie said the seven would have their first formal meeting "in a few days" time to "assign roles and responsibilities".
The group has launched a website and a twitter feed.
And the group rejected comparisons with the SDP - which broke away from the Labour Party in the early 1980s but eventually merged with the Liberal Party - saying it was a different era and they would not be contesting by-elections.
In a founding statement, the group sets out its approach to the economy, public services and security, as well as Brexit, saying its aim was to "pursue policies that are evidence-based, rather that led by ideology".
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