The ex-Manchester United executive will begin his new position on December 16th, following Rangers' League Cup final against Celtic.
Stewart replaces James Bisgrove who left the role in the summer for a move to Saudi.
Talks remain ongoing over a new permanent chairperson, with Malcolm Offord in the frame to permanently replace John Bennett, who stepped down for health reasons this season.
Stewart spent 18 years at Old Trafford - most recently as interim CEO - with the club saying that experience makes "him an excellent fit for his new role at Rangers".
TrendingThe former lawyer - who also helped negotiate contracts at United and co-led on the creation of the women's team - held various roles at the Premier League club.
He had also been a member of various working groups within the FA, the Premier League and the European Club Association, and presided over a variety of international sports disputes as an arbitrator for the Court of Arbitration for Sport.
Rangers' interim chairman, John Gilligan, said: "On behalf of the Board, I'm delighted to welcome Patrick to the club as CEO. Patrick comes with an excellent reputation and background, bringing extensive experience of operating at senior levels during his 20-plus years in football.
"The Board continues in discussions with several excellent candidates for the role of Chairperson and expect to make an announcement of an appointment in the coming weeks".
Speaking exclusively to News in September, Gilligan revealed he would stay on as chairman "for as long as it takes" and his key priority was to appoint a new CEO - adding it was his "dream scenario" to have someone in the role by Christmas.