Mogensen co-founded and was CEO of OZ Communications, a mobile software company, while still studying philosophy at the University of Iceland. He grew OZ to over 200 employees and sold over 100 million copies of its messaging software to all the major handset manufacturers and mobile operators before selling OZ to Nokia in 2008.

In parallel Mogensen also co-founded Islandssimi, which later became Vodafone Iceland, and CAOZ, an animation studio which created the first full-featured 3D animated film in Iceland, Thor - The Legends of Valhalla. Mogensen is the largest investor and board member in Carbon Recycling International which is gaining global recognition for its pioneering work in the green energy field. CRI built the first plant in the world which converts CO2 emissions into Methanol, thus converting waste into energy. In 2010 Mogensen led a group of investors to resurrect MP Bank after the total collapse of the banking sector in Iceland.

Skúli Mogensen is an active patron of the arts and has sponsored a number of exhibitions and artists in Iceland over the years. Other hobbies include extreme skiing, cycling, and triathlons. Mogensen created the WOW cyclothon, an annual, unique 1358 km ultra-cycling race around Iceland, where teams and individuals compete and raise funds towards a good cause.