Sola, who picked up a gold at last week's Cannes Lions for his work on Stella 4%, will join Fallon in the next couple of weeks.
In his new role, he will work across Fallon's client base, which includes Cadbury, Sony and Orange.
Sola, a copywriter, has already worked on the Orange business, picking up several awards on the Gold Spot account while the business was at Mother, including a yellow Pencil at the D&AD Awards last month.
The Gold Spot account moved in August last year, following Orange's decision to consolidate its business into Fallon.
Sola, who joined Mother as a copywriter in 2005, has worked on a number of other award-winning campaigns, including the Edinburgh International Film Festival-winning Eurostar-funded film Somers Town. His "Rio" campaign for Orange also secured a yellow Pencil at D&AD in 2006.