The first German troops to arrive in the country were greeted in a ceremony at the Sarajevo headquarters of the Eufor force on Tuesday, a German military spokesman said.
Germany will send 30 troops in total to the country by mid-September after leaving the country in 2012.
Bosnia is hundreds of kilometres from the fighting in Ukraine but faces an increasingly assertive Bosnian Serb separatist movement that analysts say has at least tacit support from Moscow.
Nato and senior EU officials have warned that instability from the war in Ukraine could spread to the Western Balkans.
Only days after Russia's invasion of Ukraine, the EU decided to almost double the size of its Eufor peacekeeping force to 1,100 from 600 troops by sending in reserves to stave off any instability.
During a visit to the northern town of Novi Grad on Tuesday, Bosnian Serb separatist leader Milorad Dodik said German troops were not welcome, in reference to enmity from the Second World War.
Mr Dodik has previously said he regretted agreeing as a member of the state presidency to extend the mandate of Eufor.
The peacekeeping mandate runs out in November, and it is up to the UN Security Council to decide whether to extend it for another year.
Concerns are growing in the West that Moscow might use its veto to prevent an agreement.
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The Russian embassy in Bosnia on its website decried "unacceptable references" to the impact of events in Ukraine on the situation in Bosnia.
It said Eufor had described the situation as peaceful and stable in its most recent report to the UN Security Council.
"The narrative about the need to expand the Eufor military personnel, including the German troops, is unfounded," the embassy said.
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It said some western states, mainly the US and Britain, were preparing for a "crawling Nato-isation" of Bosnia.
Eufor replaced Nato peacekeeping troops in Bosnia in 2004.
The European troops are meant to stabilise the country after Bosnia's Serbs, Croats and Bosniaks waged a war for territory in the 1990s, in which 100,000 people died.