He studied at the Royal High School, Edinburgh under the Rector Alexander Adam from 1783 to 1785, and then served as a volunteer on board HMS Culloden, under Captain Thomas Troubridge.
[1] In 1801 Greig was banished to Siberia for a time, in consequence of boldly remonstrating with the Emperor Paul for his severity to some British naval prisoners.
He was in full command of the Russian fleet, which he had brought from Sevastopol: forty vessels, eight being of the line, acting in conjunction with the troops under Prince Menshikov for three months by sea and land.
During these operations the Emperor Nicholas I of Russia was his guest on board the Parizh,[2] which had the Diplomatic Chancery and 1,300 persons under her flag.
[3][page needed] In 1833 Greig was recalled to Saint Petersburg, where the Emperor Nicholas appointed him a member of the State Council of Imperial Russia and asked him to superintend the construction of the Pulkovo Observatory.