Colless last month said he would not be seeking re-election when his term ends in February.
Pridham will step into the role having served on the Swans board for the past 12 years, while Andrew McMaster will continue as deputy chairman, the club announced in a statement on Wednesday.
Pridham is CEO of investment bank Moelis & Company and has previously served as executive chairman of J.P. Morgan and as managing director of UBS Investment Bank.
Colless said he was delighted that the two senior positions were going to be filled by sitting board members who had a strong understanding of the Swans' culture and values.
"We believe this is best achieved by, if you like, people serving a genuine apprenticeship," added Colless.
"I'm sure the handover will occur as smoothly as the Paul Roos/John Longmire transition did."
Colless assured fans that the appointments were not a sign of complacency within the board or club.
"We remain totally committed to continual improvement in all facets of our activities. To do otherwise is a guarantee for mediocrity," he said.
