Riza joined the Bluebirds from Watford at the start of the season and was asked to step up from assistant coach to interim manager when Bulut was sacked on 22 September.
Riza won four of his first seven matches, but Cardiff’s board were indecisive as the search for Bulut’s permanent successor dragged on for more than two months.
Former players and fans were critical of club owner Vincent Tan, chairman Mehmet Dalman and chief executive Ken Choo for the lack of clarity surrounding Riza’s future.
Having drawn two and lost three of their past five matches, Cardiff are 20th in the Championship table, two points above the relegation zone.
Owner Tan said: “We’ve clearly seen a change for the better in playing style and performance during Omer’s time as interim manager with some encouraging results.
“After careful consideration in recent weeks as to what the best decision was for the club and this squad of players, I’m very pleased to give Omer this opportunity and wish him well.
“Our targets, clearly, are to climb the Championship table and further develop a squad that has youth and ability at its core.
“I thank our supporters for their patience during this critical review period and hope we can all enjoy better times during the remainder of this season.”
Riza said: “I am delighted to be able to continue to lead this brilliant football club, and would like to thank Tan Sri Vincent and the board of directors for the opportunity.
“We have made real progress during the last few weeks, and I look forward to continuing our work on the training pitch over the coming months.
“I’m very excited for the remainder of the season, and hope that you Bluebirds fans are looking forward to joining us.”
