World Cup-winning coach Kirsten will take over the white-ball teams while Gillespie will look after the Test side on a two-year contract -- the first time Pakistan has employed separate coaches for different formats.
"Both Kirsten and Gillespie are famous and experienced coaches and their appointment confirms the trust the international community has in our team," Pakistan Cricket Board (PCB) chairman Mohsin Naqvi told reporters in Lahore.
Kirsten played 101 Tests and 185 one-day internationals for South Africa between 1993 to 2004 before coaching India to win the 50-over World Cup in 2011.
The 56-year-old is currently coaching Gujarat Titans in the Indian Premier League.
He will join the team on the England tour next month where Pakistan will play four Twenty20 internationals.
"Understanding the current state of the team and charting a path towards our desired goals is paramount," said Kirsten.
"Winning global events, while challenging, remains a significant objective.
"Whether it's the upcoming tournament in June or events in the future, achieving success in these competitions would be a remarkable feat."
Gillespie, 49, played 71 Tests and 97 one-day internationals in a glorious career for Australia.
He coached Yorkshire to win the English County Championship in 2014 and 2015.
"Leading the Pakistan cricket team is a big achievement for any coach, given its rich legacy and passionate fan base," said Gillespie.
"I understand there will be expectation and that comes with the role. All I can do is to take it in my stride and I would not have taken on the job if I did not think I could deal with it."
Former Pakistan all-rounder Azhar Mahmood will serve as assistant coach to both Kirsten and Gillespie.
Mahmood was interim head coach of Pakistan for the New Zealand Twenty20 international series which ended 2-2 on Saturday in Lahore.
Gillespie will join the team when Pakistan host Bangladesh and England later this year.
The arrangements are part of Naqvi's reorganisation of cricket since taking over at the PCB in February, which has seen the selection committee restructured.
Babar Azam was reappointed white-ball captain last month, replacing Shaheen Shah Afridi and players have been training at an army base to improve their fitness.
Pakistan will also play three T20 internationals in Ireland before facing England and then heading to the United States for the T20 World Cup.
