The former Cardiff winger will join the club with immediate effect but will train with the Tykes' sister Rugby League club, Leeds Rhinos, until the start of the season.
Commenting on the signing, Chief Executive Gary Hetherington said, "Liam is a great addition for the Tykes squad for the forthcoming season and we are delighted he has agreed to join us. He has expressed an interest to play rugby league and he will be joining up with the Rhinos and training with them with a view to playing with our Senior Academy from this Wednesday.
"The Tykes season starts in mid-September and he will then play rugby union throughout next season with a view to possibly coming back to rugby league next summer."
Botham, who is the son of cricket legend Ian, has recently spent a month on trial at Bradford Bulls playing in their Senior Academy and the opportunity to continue developing at Leeds was a major factor in his decision to move to Headingley.
He commented, "I have enjoyed my first taste of Rugby League and I am grateful that Leeds have given me an opportunity to continue playing the game in the off season for the Tykes.
"These are exciting times at Headingley and I am really looking forward to the next year and being part of that," added Botham.
Headingley already has a special place in the Botham family after Ian famously scored 149 not out in theinfamous Ashes Test at the stadium in 1981.