His decision comes after the Lib Dems pledged to cancel Brexit if they come to power at the next general election.
Councillor Lowe, who joined the party in 1975, follows in the footsteps of six MPs who have joined the party in the last few weeks including ex-Labour MPs Luciana Berger and Chuka Umunna and former Tories Phillip Lee and Sam Gyimeh.
The Lib Dems' Brexit announcement, as well as the 21 MPs being expelled from the party as they tried to stop no-deal, proved to be the main factors in Councillor Lowe's decision.
He said: "Conservative politics is moving much too far to the right for my liking.
"It is absolutely a wrench for me to leave after so many years, but the position adopted by the Lib Dems at conference to revoke Brexit if they achieve a majority at the next election was the clincher for me. It is time to nail my colours to the mast.
"The kicking out of the 21 rebels dismayed me. I didn't like Boris's decision."
He added: "It's been a while in gestation. It's entirely because of the national political situation. I shall be losing some friends over this decision."
Councillor Lowe joined the Conservatives in 1975. Since then, he has been chairman of the Wrekin Conservative Association from 1995 to 1997 and a Conservative Wellington Town Councillor for the Shawbirch ward since 2015.
He added: "I've been an active Conservative member since 1975, since the first referendum. That was what attracted me to the Conservative party.
"I've had to think about what my options are. It is unlikely that the Lib Dems will win a majority at the next election in our area.
"I've got the rest of my tenure as mayor until May, and I will remain a town councillor until 2023, though I'm not sure the Conservative councillors will be too pleased to welcome me back."
Councillor Greg Spruce, chairman of Telford & Wrekin Liberal Democrats, said: "We're delighted to welcome Anthony with his track record of hard work in the community. I'm looking forward to working with him.
"We've been attracting members from both parties (Conservative and Labour) for quite some time. We've had other activists and councillors get in touch. It's going to be very interesting over the next few weeks and months."
Wrekin MP Mark Pritchard said: "I wish him every success for his future. However, scores of new people have joined the Conservative Party since Boris Johnson became Prime Minister. In fact, new members are joining all the time."