Al Qassimi has to miss the event due to business commitments, leaving a vacancy in the car Citroen runs under the Abu Dhabi banner.
Meeke, the 2009 Intercontinental Rally Challenge champion, has not had a top WRC seat since the Prodrive Mini programme was cut back at the end of 2011.
"This is an incredible opportunity for us," said Meeke.
"Taking part in Rally Finland in a DS3 WRC is a dream that I didn't think would become reality one day.
"We're going to benefit from the advice and expertise of a team that has won the world championship eight times. We therefore have every chance of securing a good result."
Al Qassimi said he was excited to see what Meeke achieves in Finland.
"Kris has real potential as a driver and has the maturity you need to enjoy a sensible and efficient race," he said.
"I'd like to give him the chance to express himself fully at this unusual event. I hope he is very successful there."
Meeke's main programme this season is testing with Peugeot ahead of its return to top-level rally with its new R5 car. He is driving the R5 as a course car on the European Rally Championship round in Ypres this weekend.