Riza joined the Bluebirds from Watford at the start of the season and was asked to move from assistant coach to interim coach when Bulut was sacked on 22 September.
Riza won four of his first seven matches but Cardiff’s board was indecisive as the search for Bulut’s permanent successor dragged on for more than two months.
Former players and fans criticized the club’s owner Vincent Tan, president Mehmet Dalman and chief executive Ken Choo for the lack of clarity surrounding Riza’s future.
After drawing two and losing three of their last five games, Cardiff sit 20th in the Championship standings, two points above the relegation zone.
Owner Tan said: “We have clearly seen a change for the better in playing style and performance during Omer’s time as interim coach with some encouraging results.
“After carefully considering over recent weeks what was the best decision for the club and this team of players, I am very pleased to give Omer this opportunity and wish him the best.
“Our objectives, clearly, are to move up the Championship table and further develop a team that has youth and skill at its core.
“I thank our fans for their patience during this critical review period and hope we can all enjoy better times during the rest of this season.”
Riza said: “I am delighted to be able to continue leading this brilliant football club and would like to thank Tan Sri Vincent and the board for the opportunity.
“We have made real progress over the last few weeks and I look forward to continuing our work on the training pitch over the coming months.
“I’m really excited for the rest of the season and I hope the Bluebirds fans can’t wait to join us.”
