The Football Association of Wales have confirmed Rowberry will remain in his role as Craig Bellamy's assistant with the Wales national team.
Robins led the Sky Blues to promotions from League Two and League One and reached the Championship play-off final in 2023, where they lost to Luton on penalties.
They failed to match that top six finish last season but did take Manchester United, where Robins started his playing career, to a penalty shootout in the FA Cup semi-final.
He has also had spells in charge of Rotherham, Barnsley, Scunthorpe and Huddersfield.
Stoke started the season under Steven Schumacher but sacked him in August to appoint former Huddersfield and Norwich coach Pelach.
However, they won just three of his 19 games in charge and the 36-year-old was sacked on 27 December after a 2-0 home reverse by Leeds stretched their winless run to nine matches.
Robins is now the club's seventh managerial appointment since their 10-year spell in the Premier League came to an end in May 2018.
They are yet to finish in the top six of the Championship since being relegated.