Vengloš was appointed as Head Coach of Celtic on 17 July 1998. Season 1998–99 saw his Celtic team in some excellent form, but they failed to qualify for the Champions League. At the end of the season, Vengloš left to take up a new position as a European technical adviser and as a scout for Celtic. He is most credited with signing fans' idol Ľubomír Moravčík during his season as manager. Other successful signings include club legend Johan Mjallby and while a trophy evaded Vengloš, he is still looked upon fondly by fans for bringing such players to the club. The stand-out of his reign came as his Celtic side inflicted a punishing 5–1 defeat on arch-rivals Rangers in the first half of the season. In the new year of 1999, he also took Celtic to Ibrox where they held their Old Firm rivals to a 2–2 draw on their own soil.