Wittmann secured the DTM crown in commanding fashion, clinching the title with two rounds to spare thanks to four wins in what was only his second season in the tin-top category.
As well as arranging the Toro Rosso test, BMW has also agreed a new contract that will keep the 24-year-old on their books through 2015 and beyond.
"Marco Wittmann has an extraordinary season behind him, in which he has given BMW Motorsport an awful lot of pleasure," said BMW motorsport boss Jens Marquardt.
"It is now our turn to reward him for his efforts. The contract renewal for the coming season is a logical step for us, as he has consistently impressed us in the three years he has been working with us within the DTM - both on and off the track.
"For this reason, BMW M GmbH has come up with something very special. I am delighted that we can also make his childhood dream come true with the Formula 1 test.
"Thanks to the relationship we enjoy with our premium partner Red Bull, it was possible for us to organise a test drive in the Toro Rosso.
"We are excited to see how he fares in this car - and are then looking forward to more top-class performances from Marco in the BMW M4 DTM."
“I am overwhelmed,” added Wittmann.
“The entire season has been incredible. After all, coming into the opening race of the season here in Hockenheim, I never believed I would be standing here in the same place as the DTM champion.
"And then to have my contract as a BMW works driver renewed and receive a Formula 1 test – that is a dream come true for me."
Prior to switching to tin-tops, Wittmann competed in junior single-seater racing, finishing as runner-up in the F3 Euro Series in 2010 and '11