I see from the Tamriel map that it would be a long journey east or west by ship to get to Vvardenfell from Cyrodil but there is alos a large mountain range between Cyrodil and Morrowind so how did the Imperilas get there in the first place? Ship seems to be feasible but slow so did they take Morrowind first and then moe into Vvardenfell?

There are several passes through Velothi mountains and major roads connecting Cyrodiil and Morrowind.
At the time of Tiber Septim's conquest of Morrowind Skyrim was already part of the Empire and his troops could launch invasion from there as well.

Don't trust everything you see in games, game mechanics and sandbox approach ruled out "realistic" borders.

When it comes to Vvardenfell, Empire gained foothold at much later date, originally it was Tribunal Temple's Reserve with limited Imperial influence.

A wizard did it.... Alteration is your friend. Passwall....Water Walking.... easy trip.

If you look at some maps, you'll notice a few significant towns near the border of Morrowind and Cyrodiil. Those very likely cover passes through the mountains. Significant passes in which armies could likely travel through.

Also, Tiber Septim never actually invaded Vvardenfell. They had roughly siezed the NorthWestern-Western corner of Morrowind when the Tribunal signed the Armistice, granting Imperial troops rights of occupation.

So, in answer to your question, they used a boat.