Grant, who led Chelsea to the 2008 Champions League final and kept them in contention for the Premier League title until the last day of the season after taking over from Jose Mourinho, was appointed on Friday after Aleksandar Stanojevic's sacking.
"We are in a good position to win the league and our first task is to retain the title before we aim to qualify for the group stage of either competition in Europe next season," Grant told a news conference in Partizan's Teleoptik training centre.
"I know the targets set by the club president will bring a lot of pressure but that is why I am here because pressure is always a part of football at the top level."
"I am happy to be in this city and to have come into this club with a great name and tradition, I like their vision of producing and developing players," he said.
"For me it will be a big challenge because football is all about challenges and mine is to prepare this team for competition in Europe.
"It is very important that young players here are willing to learn and achieve results and for this we need a strong team with some experienced players in the squad too."
Stanojevic was sacked after a rift with the club's board over the dismissal of managing director Mladen Krstajic last month following his conflict with president Dragan Djuric.
Grant's contract at Chelsea was terminated after he conceded the Premier League and Champions League titles to Manchester United in 2008 and following an eight-month spell at Portsmouth, he failed to save West Ham United from relegation last season.
