Castle ward councillor and cabinet member for resources, Dan Humphreys, was elected by his colleagues at a private meeting on Monday night.
After a week of speculation over who would take the helm, Mr Humphreys eventually stood unopposed to claim the job.
A full council meeting will be held later this month to approve him as leader, with Mr Yallop steering the rudder in the meantime.
He said: “It’s humbling and lovely to have been asked by my colleagues to lead the group. It’s exciting and I am now motivated to get on and deliver the best for Worthing.
“I genuinely woke up this morning before the alarm clock and bounced out of bed with real energy.”
Mr Humphreys was elected in 2011, grabbing the seat from the clutches of the Liberal Democrats by 85 votes.
He later missed out on the Northbrook county council seat by just five votes to the same Lib-Dem candidate – Robin Rogers.
His predecessor, Mr Yallop, promoted him to the cabinet in 2013 and recognised his potential early on.
He said: “I promoted him to the cabinet and saw he had potential then, so he attended a future leader course.
“I think you need a calm attitude and you need to listen and communicate well with people.
“Clearly, to have that, you have to have the determination to deliver good things for the people you are serving.”
Lib-Dem leader Keith Sunderland said he was pleased with the opposition’s choice and felt he could work with him.
“He is young and inexperienced, but I think he might rise to the challenge.
“Being council leader is a pretty thankless task. You get all the blame and the flak and sometimes have to make difficult decisions.
Fellow ward councillor Luke Proudfoot said his colleague had a ‘true dedication’ to Worthing and would make a ‘great leader’.
Mr Humphreys plans to keep Bryan Turner as deputy and will not make large-scale changes to the cabinet.
He is up for election in May.