Newport were four points adrift of safety in the fourth tier when Fuchs was named as Dave Hughes’ successor in November last year.
The Austrian guided Newport to survival in League Two, but left the club on the eve of their return for pre-season ahead of the 2026-27 campaign.
The arrival of Mullins means it is the third successive summer that there has been a managerial change at Rodney Parade.
He is also the fourth permanent boss appointed by owner Huw Jenkins since his January 2024 takeover of the club, following Nelson Jardim, Hughes and Fuchs in the hot seat.
Former England Under-21 international Mullins – who also played for Reading, Birmingham City and Notts County – moved into coaching within Watford’s youth system in 2016.
Having managed the Hornets’ under-23s, he twice took temporary charge of Watford’s senior team, following the exits of Quique Sánchez Flores and Nigel Pearson from Vicarage Road.
Mullins joined Colchester United as an assistant in 2020 and – following a stint as interim boss – took permanent charge of the U’s in May 2021, but was sacked less than a year later.
He went on to have a brief stint in charge of the Turks and Caicos Islands national team in 2023 before joining Fulham as under-21 boss later that year.
In his first campaign in charge, Mullins led the young Cottagers to Premier League Cup glory with a 4-0 victory over Tottenham Hotspur Under-21s in the final.