Former Gills defender Pennock, 45, will be joined by Welling United boss Jamie Day and Bromley assistant manager Steve Lovell as first-team coaches.
The trio have been placed in charge until the end of the season.
"A change was necessary to ensure the club achieves the best possible position," said chairman Paul Scally.
"The current squad is the most expensive in the history of Gillingham FC, it has enormous potential and is capable of achieving great success over the remainder of the season and beyond."
Prior to Wednesday's appointments, Scally told BBC Radio Kent he may change the club's management structure, adding: "We may have a head coach and a team of coaches, with a director of football."
Former Welling boss Pennock was sacked by Forest Green before the National League play-offs in April despite securing second place in the table, having been in charge since 2013.
Pennock was assisted by Day - who previously played under him at Welling - at Forest Green.
Former Wales and Crystal Palace striker Lovell spent five seasons playing for the Gills and has previously taken caretaker charge of the club.
In a statement, Bromley manager Neil Smith said: "I'm obviously disappointed to lose Steve from our management team but at the same time I'm delighted for him to return to his home club Gillingham. I wish him all the very best."
League One side Gillingham have named former Forest Green Rovers boss Ady Pennock as their new head coach, after sacking Justin Edinburgh on Tuesday.