He fills the gap left by Chris Moss' promotion to European chairman in March. The Number's finance director Tyrone Davies has been acting chief executive for the last three months.
Horgan will start at the end of August with the brief to focus on the UK market. The Number is looking to double the size of its business over the next two to three years.
He will work closely with The Number's creative agency WCRS, which created the 118 118 runners campaign. The business uses Naked and OMD UK for its media planning and buying.
Horgan joined MFI in 1999 from Mars Confectionery Europe where he was responsible for the global marketing of the Mars bar. Before that he was joint marketing director of McVitie's UK.
The Number is set to expand into several European markets this year. Moss is spearheading the development of The Number's French directory enquiries service Le Numero and the Il Numero offering in Italy.
Horgan was instrumental in MFI's attempts to transform its brand image over the past few years, from "made for idiots" to fashionable and style-conscious. He helped it reverse losses to rivals such as Ikea.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the Forum.