Merz secured the necessary absolute majority to succeed outgoing Chancellor Olaf Scholz in the second round of voting, receiving 325 votes in the 630-seat Bundestag, Germany's lower house of parliament.
Merz initially won the backing of only 310 MPs in the first vote, falling short of the absolute majority by six votes.
Scholz congratulated Merz in the Bundestag after the second vote on Tuesday.
Merz's failure to win parliamentary backing at the first time of asking was a first for post-war Germany and an embarrassment for a man who has promised to revive economic growth at a time of global turbulence.
His CDU/CSU alliance won February's federal election and secured a coalition deal with the progressive Social Democrats.
Their deal has mapped out plans to revive growth, such as reducing corporate taxes and lowering energy prices.
It is also promising strong support for Ukraine and higher military spending.
Merz, 69, who began his political career as a European MEP in 1989, has yet to demonstrate his leadership abilities in the political executive as his appointment marks his first time holding a government office.
Only one minister from the previous government will retain his position, Defence Minister Boris Pistorius.
The rest of Merz's cabinet are new appointees, many with private sector experience.
with DPA
