The Remain voter and Labour supporter was joined by Eloise Todd, the new chief executive of Best for Britain.
Miller thanked the thousands of people who have donated almost £300,000 (€350,000) to the campaign in just a week.
The businesswoman also ruled out standing in the 8 June vote, but urged the British electoral to vote tactically for candidates "with an open mind" in a bid to avoid an "extreme Brexit".
"We will support candidates who campaign for a real final vote on Brexit, including rejecting any deal that leaves Britain worse off," she said. The launch saw Best for Britain unveil its three-point charter.
"People across the UK must be able to rely on their MPs to reject any deal that does not measure up as best for Britain. No one should have to sign a blank sheet of paper," the document said.
Miller hit the headlines in 2016 when she took the government to court over May's plan to enact Article 50 of the Lisbon Treaty without giving parliament a say on the Brexit trigger. Miller and her legal team came out on top and MPs and peers eventually backed the government's Article 50 bill.
The prime minister said she called for the general election in a bid to strengthen her hand at the Brexit negotiating table with the EU. "The country is coming together but Westminster is not," May declared.
The vote could also see the Conservative premier dramatically increase her slim working majority in the House of Commons from f just 17 MPs.
The latest opinion poll from ICM, of more than 2,000 people between 21 and 24 April, put the Tories 21 points ahead of Labour (48% versus 27%), suggesting May could win a majority of more than 100 MPs.