Gisdol was dismissed following Sunday's 3-2 home defeat by Mainz and Funkel, 67, has been tasked with keeping Cologne up in his second spell at the club having been head coach for an 18-month spell until October 2003.
"Friedhelm doesn't just have a lot of experience, but is also someone you can really trust in a situation like this," said Cologne's managing director Horst Heldt.
"He will coach our team until the end of the season, with the goal of staying up."
Cologne, who are in their second season back in the top flight since promotion in 2019, sit second-from-bottom in the table, three points behind Arminia Bielefeld who occupy the relegation play-off spot.
"With a change of coach, we want to give the team a new boost," added Heldt.
Funkel has come out of retirement having said he was quitting after being sacked in January 2020 by Cologne's rivals Fortuna Duesseldorf, who were ultimately relegated last season.
Gisdol took over at the RheinEnergieStadion in November 2019, helping Cologne avoid relegation in 2019/20, but paid the price after six defeats and only one win in their last nine games.