Two British naval ships are shadowing the vessels. The Ministry of Defence said they would be "man-marked every step of the way" while near UK waters.
A Russian tug, believed to be in convoy with the taskforce, entered the channel first off the coast near Ramsgate.
EU leaders have strongly condemned Russia's involvement in bombing the Syrian city of Aleppo.
The ships are within international waters but Defence Secretary Michael Fallon said the UK would "be watching as part of our steadfast commitment to keep Britain safe".
