Bosnia international impresses manager in Premier League opener and is expected to have a bigger role in side.
Pellegrini expects great things from Dzeko after Newcastle thrashing
Dzeko joined City from Wolfsburg in a £27 million (Dh155m) deal in January 2011 but the striker has struggled to establish himself as a regular starter.
The 27 year old was City's top goal-scorer in the Premier League last season with 14 goals, yet had been tipped to move on following the arrivals of highly-priced forwards Alvaro Negredo and Stevan Jovetic in pre-season.
But when Pellegrini took over as Roberto Mancini's replacement he made it clear that he wished to keep hold of Dzeko.
The Bosnia international responded by delivering an impressive pre-season and put in an outstanding performance after starting in City's 4-0 win over Newcastle United in their opening match of the Premier League campaign on Monday.
He was unfortunate not to score himself but showed real energy and desire against Alan Pardew's side.
And Pellegrini feels Dzeko, who has also stated he thinks the new manager will get the best out of him, will now be able to show what he is capable of.
"I trust a lot in Edin Dzeko. It was a pity he didn't score against Newcastle because he had a lot of chances, he played very well," Pellegrini said.
"With the ball we all know he is a very good player but he also played without the ball. He worked a lot on trying to recover the ball in attack and after that, he had three or four important chances and deserved to score a goal.
"I am sure we are going to see this season the Edin Dzeko that Manchester City bought two years ago from Wolfsburg.
"I spoke with him the first day I arrived here and I am sure we will see the Dzeko all of you are waiting for."
Although Pellegrini is now awaiting news of Vincent Kompany's groin problem, which he fears could keep the City captain out for up to two weeks, it could not have been a better start for the new manager.
David Silva scored the opener against Newcastle within six minutes and Sergio Aguero doubled the advantage before Steven Taylor was sent off for striking Aguero with his arm.
Yaya Toure's free-kick and a simple finish for Samir Nasri completed an emphatic victory, but Pellegrini is adamant there is much more to come from the team as they adapt to his style.
"I don't think it is a dream start but it is a very good start," he said.
"I was very confident the team would play well. We worked very hard during pre-season, trying another style of football and maybe we can continue improving every week.
"For the first match I think we did it very well."
Pardew spurns Arsenal interest in Cabaye
Meanwhile, Newcastle manager Alan Pardew believes the transfer window should close before the start of the season after Arsenal's bid for Yohan Cabaye on Monday disrupted his game-plan.
The Gunners made a £10m offer for the France midfielder Cabaye, 27, hours before the match and Pardew left him out of the squad as a result.
Following the transfer sagas involving Luis Suarez, Gareth Bale and Wayne Rooney this summer, Pardew, who accused Arsenal of a lack of respect, wants a change in regulations.
"This is a terrific player. You put him in the same situation as Suarez and Bale," Pardew said.
"There is a question about the window being closed before we kick off the Premier League season.
"I know the Premier League asked the European leagues to do it and they said the European leagues wouldn't fall in line.
"After the summer we have had, the situations we have had, with Rooney as well, it is definitely something they need to put under the microscope again."
Follow us @SprtNationalUAE