The 39-year-old, who appeared for the club between 1987 and 1989, is already a Director of London Irish Holdings plc and was an acclaimed international centre during a Test career that lasted from 1984 to 1995 and included a Lions tour.
The Managing Director of Powerscourt Capital Partners, a Dublin based fund management business, Mullin replaces John Conlan and Kevin Clancy who have been joint Chairmen of the club over the past two years, although both will continue as vice-Chairmen.
In addition to Mullin's elevation, Paul Theaker has been named as Finance Director and Patrick Coyne becomes Commercial Director, both men serving under recently-appointed Managing Director Conor O'Shea.
Meanwhile, on the playing front, coach Brendan Venter has made three changes for this Sunday's home Zurich Premiership clash against the Sharks.
All the changes are due to squad rotation, with Rob Hardwick, Richard Kirke and Kieron Dawson starting in place of Simon Halford, Naka Drotské and Declan Danaher respectively.
London Irish: 15 Mark Mapletoft, 14 Paul Sackey, 13 Nick Burrows, 12 Brendan Venter, 11 Michael Horak, 10 Barry Everitt, 9 Hentie Martens, 8 Chris Sheasby, 7 Kieron Dawson, 6 Paul Gustard (captain), 5 Nick Kennedy, 4 Bob Casey, 3 Rob Hardwick, 2 Richard Kirke, 1 Mike Worsley.Replacements: 16 Kevin Barrett, 17 Geoff Appleford, 18 Glenn Delaney, 19 Adrian Flavin, 20 Declan Danaher, 21 Neal Hatley, 22 Simon Halford.
Kick-off: 15.00 GMT