Striker Stevenson – who has also previously served Ashfield – arrives at John Cumming Stadium after not playing for Forth in the campaign just finished due to injury issues.
“Billy brings a wealth of experience at our level, ”Davies said.
"I have spoken to him over the past couple of weeks. We hope he’s going to be an influential player in the team.
"Billy is an old fashioned type centre forward. He’s a strong lad who is a proven goalscorer.
"Billy was definitely a player we targeted and to get it across the line has been brilliant.
"We are sitting with about 12 or 13 in the squad at the moment.
"The aim for next season is to make sure we’re competing in the top half of the league.
"And in terms of squad wise we are hoping to bring in another four players.”
After a topsy-turvy campaign, Rovers finished 11th in Conference B of the 2021-22 West of Scotland League campaign just finished.
Former Newmains United gaffer Davies and his fellow co-manager Craig Gupwell landed their roles at Carluke in February – two months after Mark Weir quit as gaffer and Kenny Neill took over in an interim capacity.
The new management team made their first signing late last season with the arrival of midfielder Michael Barton who played in the final two league games, scoring a goal against Royal Albert.
Meanwhile, Davies revealed that plans are being made towards ressurecting the Clydesdale Cup, involving Rovers, Lanark United, Lesmahagow Juniors and Forth Wanderers.
The traditional curtain raiser to the new football campaign for the four local sides hasn’t taken place in each of the past two years due to the ongoing effects of the coronavirus pandemic.
But, with all restrictions now finally eased after a miserable run of disruption, it could be back on the calendar this year.
"If we could get the Clydesdale Cup up and running again it would be good because it sorts out pre-season friendlies,” Davies added.