The 26-year-old Dutchman, formerly of Feyenoord, Real Madrid, Everton and Alania Vladikavkaz, has impressed at the Madejski Stadium since manager Nigel Adkins snapped him up in the summer.
"I thank the gaffer, the coaches and everyone who has worked really hard with me," he said.
"It was really tough in pre-season but I'm in good shape and I feel really good. I said to my team-mates that I'm really happy to be here and I hope that I can be here for a long time."
Next up for Drenthe is a trip to Blackpool as the Royals look to maintain their unbeaten start to the campaign.
"Blackpool is the next game and we have to be confident," he added. "It will not be easy against them, they are on an up at the moment. We have to go there and prove ourselves."