British military personnel have started training members of the Ukrainian army fighting pro-Russian rebels, the BBC has learned.
The 35 trainers are working in the southern city of Mykolaiv and will spend about two months in the country.
They will train forces in eastern Ukraine in medicine and defensive tactics and give non-lethal equipment.
The Ukrainian PM said he "truly appreciated" the support, while the deployment was criticised by Russia.
The deal was announced by Prime Minister David Cameron last month.
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.
According to a report in the Wall Street Journal, the Pentagon has delayed a training programme for Ukrainian soldiers because it fears it could give Russia a reason to end the the current peace deal.
A ceasefire took effect on 15 February following an agreement reached in Minsk, Belarus, and has largely held despite sporadic shelling.
The British government is also supplying first aid kits, sleeping bags and night-vision goggles as part of its pledge to provide assistance and more British teams are expected to arrive in Ukraine over the coming weeks.
BBC correspondent Tom Burridge said the deployment of dozens of military instructors was a symbolic move that would not alter the military balance of the war.
The Ukrainian Prime Minister Arseniy Yatsenyuk welcomed the assistance in his country, which he said was defending "peace and stability" in Europe.
He told the BBC the trainers would "help increase the durability of the Ukrainian military".
Mr Yatsenyuk said he saw the help as a "first step" and expected further assistance would come from other EU countries and the US, adding: "Please help us to defend our country and your peace."
Conflict zone tension
Dmitry Pveskov, press secretary to President Putin, told journalists the deployment would not relax tensions in the conflict zone.
He said: "A presence of foreign instructors in Ukraine cannot facilitate the settlement of the conflict in this country.
"Of course, it has been stated repeatedly that it does not contribute to the strengthening of trust or relaxation of tension in the conflict zone.
"It can be clearly said that it does not contribute to the settlement."
The United States has already said it is planning to send a battalion to train three Ukrainian battalions.
More than 6,000 people have died since the fighting in Ukraine erupted last April, the UN has estimated, although the organisation believes the real figure could be considerably higher.