Pennock, 46, was placed in charge until the end of 2016-17 following Justin Edinburgh's departure on 3 January.
The ex-Forest Green manager guided the Gills to 20th in League One, one place and one point above the drop zone.
Taylor, 64, returns to "oversee recruitment and all footballing policy" after two spells managing the club.
During his first stint in charge, Taylor led Gillingham to promotion to the second tier via the old Division Two play-offs.
He was reappointed as boss in November 2013, but was sacked after 14 months in charge.

Chief executive Karl Koehler is standing down and his replacement will not have a position on the main Tata board in Mumbai, unlike Mr Koehler.
Tata is making 1,050 people redundant, including 750 at its Port Talbot site.
Community organiser Rob Edwards said he was surprised by Mr Koehler's departure and what it meant for the future.
"I think it compounds the recent news about the redundancies. You start to ask questions about long-term investments," said Mr Edwards.
"There is an element of doubt, we walk a path of uncertainty," he told BBC Radio Wales's Wales at Work programme.
He added that he wasn't concerned about the short-term commitments made by the company as it tries to save Â£300m as part of its current survival plan.
He said the union was worried that the move weakened the voice of the European operation when it came to decisions being made by the board in future.
Workers from Tata marched through Brussels with Mr Koehler and steelworkers from across Europe demanding that the EU take action on the price of Chinese imports.
New chief executive of Tata Steel Europe, Hans Fischer, takes over on 1 March.
Koushik Chatterjee, the group executive director for finance and corporate affairs, will add responsibility for Europe to his role on the Tata Steel board in Mumbai.

The rare mineral, only found beneath Treak Cliff Hill, near Castleton in the Peak District, is so called because of its distinctive colour.
The new vein has been named the Ridley Vein after Gary Ridley, the miner who found it after attempting a new mining method with a stone chainsaw.
He said he could not "believe his eyes" when he came across the Blue John.
The stone was fashionable during the Regency period in the early 1800s and is displayed at Buckingham Palace and Chatsworth House.
Mr Ridley, who manages Treak Cliff Cavern, said he tried out the new saw near the tourist route.
"Having spotted a small amount of crystallisation near the handrail it was just an easy and convenient place to see how well the saw would cut...
"I couldn't believe my eyes when within a few minutes I had uncovered a substantial deposit of Blue John unlike any other vein I had ever seen before."
Vicky Turner, whose family have owned and managed Treak Cliff Cavern since the 1940s, said the Ridley Vein has "swirling patterns of purple and blue" and will be made into decorative bowls and other pieces.
Each vein has its own colour and banding of blue, purple, yellow and white. Historically, there have been 14 distinct veins of Blue John including Millers Vein, Treak Cliff Blue Vein, 5 Vein, 12 Vein and Old Tor Vein.
The Ridley Vein has now entered the record books as variant number 15.
Gillingham have confirmed Ady Pennock will stay on as head coach next season, with former boss Peter Taylor returning to the club as director of football.
[NEXT_CONCEPT]
Changes at the top of Tata Steel Europe raise doubts about the "long-term investment" of the company, according the steelworkers union, Community.
[NEXT_CONCEPT]
A vein of Blue John stone has been found in Derbyshire, 150 years after the last discovery.