He has been managing director of the business for 10 years and will now sit on the executive board of parent company Scottish Media Group.
Costello left SMG after the company decided to disband its Out of Home division, which she ran. The division brought together Primesight and cinema sales house Pearl & Dean, which will now be run as separate businesses.
Patel's first move has been to reorganise the Primesight sales team. Trading and strategic sales have been divided into separate functions. The 10-strong trading unit will be headed by Matt Stubbings and will be responsible for all rate negotiations.
Simon Armstrong, whose background was in TV sales at Carlton, will run the 20-strong strategic sales unit. Both will report to sales director Nigel Clarkson, who has expanded his remit to cover marketing.
Patel, who sold Primesight to SMG in 1999, said: "We need to get higher up the ladder with agencies and specialists. The strategic sales team is tasked with doing that without worrying about admin. They will be focused on selling as opposed to trading."
Primesight is the UK's second largest six-sheet owner, along with JCDecaux. Clear Channel is the largest player in the market.