The 35 personnel are based in Mykolaiv, in the south of the country and are expected to be in the region for the next two months.
The team will be training forces engaged in battles in eastern Ukraine in medicine and defensive tactics, and supplying non-lethal equipment.
Defence Secretary Michael Fallon announced last month that the UK would sent up to 75 troops and military staff to the war-torn country.
He said they would offer advice and training to government forces there in an attempt to boost their resilience while also reducing fatalities and casualties.
An MoD spokeswoman said: “The UK is committed to supporting Ukraine’s sovereignty, independence and territorial integrity in the face of Russia’s aggression.
“The gifting of non-lethal equipment is designed to prevent further Ukrainian fatalities and casualties and to help improve situational awareness on the ground.
“Our overall aim is to strengthen the defensive capability of the Ukrainian armed forces and build the resilience that they need.”
The British government is also supplying first aid kits, sleeping bags and night-vision goggles to the country.
It is the first time a Western nation has conducted a long-term military training programme in Ukraine since its war against pro-Russian rebels began last year.
More than 6,000 people have been killed since fighting broke out last April, but clashes have reduced since a ceasefire was declared last month.
As part of the training programme, more British teams are expected to arrive in Ukraine over the coming weeks, and the United States has also said it is planning to send a battalion to train three Ukrainian battalions.
Source: London Evening Standard