Russo's brother Vince will become executive vice-chairman to cap the pair's long-standing interest in the club.
Jimmy Russo said: "I am delighted to take on the chairmanship of such a great club.
"It's truly an honour and I look forward to working with my fellow directors. I will always do my utmost for the club and serve it in a way the fans should be proud of.
"However I want people to be under no illusions as to the task ahead."
Simpson stepped down at an Extraordinary General Meeting of the Championship club's shareholders in a bid to keep disruption at Vicarage Road to a minimum in November.
The meeting was called by the Russo brothers, who own nearly 30% of the club's shares through their company, Valley Grown Salads.
The brothers had proposed a vote of no confidence in the club's directors but Simpson's shock announcement stopped such a vote going ahead.
Former manager Graham Taylor returned to the club's board as a non-executive director last month and will remain in the position under Russo.
The new chairman also praised manager Brendan Rodgers for the recent upturn in results which has strengthened the club's league position.
Rodgers was appointed by Simpson just five days before his departure but Russo hopes that he will stay for the long term.
He said: "I am really most pleased that we have Brendan Rodgers on board for the future.
"With some hard work that future can now be one to look forward to."