Reckless, who defected from the Conservatives in 2014 and later lost his Rochester and Strood seat at the 2015 general election, said it was "job done" after Leave won the EU referendum and Theresa May had invoked Article 50 of the Lisbon Treaty.
"For me it is job done now that Article 50 has been triggered. I campaigned all my adult life for us to leave the EU. Now we are under a Conservative government," he wrote in a statement.
"I support Theresa May, and her team of Brexit ministers, to deliver. As a country it is right that we seek a sensible settlement with the EU, rather than no deal.
"As a country it is right that we seek a sensible settlement with the EU, rather than no deal."
The ex-solicitor, 46, was elected as a representative of South Wales East in 2016. Reckless said he would join the Conservative group in the Welsh Assembly.
"The UK Conservative government is getting out of the EU and I want to back it. In Wales, the Conservatives are the main opposition to Labour. It is time that was properly reflected in the Assembly," he added.
The move comes after Carswell, Ukip's sole MP, resigned from the party in March. Like Reckless, he defected from the Tories to Ukip in 2014 to put pressure on David Cameron to hold an EU referendum.
"We are disappointed to hear that Mark Reckless has decided to leave Ukip in order to join the Conservatives in the Welsh Assembly," Ukip chairman Paul Oakden said.
"When Mark joined Ukip in 2014 we admired his long-term commitment to Brexit and his decision to put his country first.
"Having been elected as a Conservative in Rochester & Strood, Mark didn't think it right to sit as an MP for another party without asking the electorate for their endorsement in a by-election.
"A position that was right as it was honourable. In the campaign that followed, our membership worked incredibly hard to ensure that Mark retained his seat.
"After losing his seat at the general election, Mark was a popular colleague and a diligent head of policy for the party, before being awarded a top position in the Ukip list for the Welsh Assembly Elections in 2016.
"Those elections gave voters in Wales the opportunity to support a party rather than a particular candidate and one in eight voters backed Ukip As a result, Mark was one of two Ukip candidates from South Wales East elected to the Senedd.
"It is now incumbent on Mark Reckless to relinquish a position he has only by virtue of a Ukip mandate. The position should go to the next Ukip candidate on the regional list."