Chelsea confirmed the decision on Wednesday morning, citing results and performances that have "fallen below the necessary standards." Rosenior arrived from sister club Strasbourg in January on a six-year contract worth around £4 million per season, replacing the sacked Enzo Maresca.
His final match was a 3-0 defeat at Brighton on Tuesday, Chelsea's fifth consecutive Premier League loss without scoring. The club could face a compensation bill of up to £24 million.
The statement added that ownership will take time for "self-reflection" before appointing a successor, signalling a potential shift in strategy.
Both Maresca and Rosenior arrived without Premier League experience, a pattern the club are now considering departing from. Co-owner Behdad Eghbali has also indicated a move away from the youth-heavy recruitment model, saying the club will pursue more "ready-made" players this summer.
Iraola is leaving Bournemouth when his contract expires in the summer, having turned down the club's attempts to extend his deal.
He is the current frontrunner for the role, with BBC Sport also naming Marco Silva and Edin Terzic as candidates under consideration.
Calum McFarlane, who took temporary charge in January before Rosenior's arrival, will manage the remainder of the season starting with Sunday's FA Cup semi-final against Leeds at Wembley.