The visit comes a week after undocumented migration to the UK was high on the political agenda during a state visit to Britain by French President Emmanuel Macron.
As well as signing the first "friendship treaty" between their countries, Starmer and Merz were expected to unveil a new deal to jointly produce defence exports such as Boxer armoured vehicles and Typhoon jets.
They were also expected to commit to developing their deep precision strike missile with a range of more than 2,00 kilometres (1,250 miles) in the next decade.
"Chancellor Merz's commitment to make necessary changes to German law to disrupt the supply lines of the dangerous vessels which carry illegal migrants across the Channel is hugely welcome," Starmer said ahead of the visit.
His office said it was hoped the German legal changes could be made "this year".
Undocumented migration has become a major headache for Starmer's year-old Labour government, as support for the upstart anti-immigrant Reform UK party soars.
More than 22,500 would-be asylum seekers have arrived on England's southeastern coast by small boat from northern France this year alone.
The "friendship treaty" also seeks to improve post-Brexit ties with its neighbours.
- Brexit trauma -
Macron's trip was the first state visit by a European Union head of state since Brexit -- the UK's acrimonious 2020 departure from the bloc.
A German government source said of the visit "we shouldn't underestimate" how much relations with the UK had improved since the "traumatic" experience of Brexit.
Starmer said the accord would be a "foundation on which we go further to tackle shared problems", echoing last week's Anglo-French talk of common challenges.
The two leaders were also to discuss continued support for Ukraine, with both London and Berlin expected to play a role in US President Donald Trump's plan to send weapons to Kyiv with financing from other NATO countries.
The visit is Merz's first to the UK as chancellor, although he has already met Starmer several times, including on a trip by train to Ukraine just days after he took office in early May.
The wide-ranging new treaty between Germany and Britain will refer to the turbulent security situation that both countries face and include a mutual defence pact.
"There is no strategic threat to one which would not be a strategic threat to the other," the text was expected to say, alongside a pledge that the two countries "shall assist one another, including by military means, in case of an armed attack".
While Britain and Germany already have a commitment to mutual defence as NATO members, the treaty is expected to pave the way for greater defence cooperation, including in weapons development and operations on NATO's eastern flank.
The two countries already signed a landmark defence agreement in October and in May said they would begin developing the strike missiles.
- Train links -
German Foreign Minister Johann Wadephul was to accompany Merz on the visit and was expected to meet his British counterpart, David Lammy.
On migration, Merz's government is expected to make a commitment to modify German law by the end of the year to criminalise the facilitation of "illegal migration".
This will include action against storage facilities used by migrant smugglers to conceal small boats intended for Channel crossings.
On transport, the two countries will commit to improving train connections.
Last month Eurostar said it planned to launch a new route from London to Frankfurt in the early 2030s, which would be the first such direct connection between the UK and Germany.
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