The flow of narcotics from Mexico to the US, as well as the flow of Mexicans themselves, will top the agenda in talks with President Ernesto Zedillo. But the three-day visit will be largely symbolic, the start of a long- delayed effort by Mr Clinton to tighten trade and other ties with the nations to the south.
Critics say he is somewhat late. Since he led a so-called Summit of the Americas in Miami in December 1994, pledging a pan-American free trade zone within a decade, he has largely neglected Latin American nations and seen Europe muscle in.
The European Union did more trade with the South American common market - known as Mercosur - than did the US last year for the first time.
"They [the Americans] only turn to look at our countries when there are wars, conflicts or natural disasters," Nicaraguan President Arnoldo Aleman said recently.
Mr Clinton will be welcomed politely, but not particularly warmly in Mexico, where people still dream of going north to prosperity but where stories of the two countries' 19th century war are still handed down from generation to generation.
"I don't see it as a visit of reconciliation," Mr Clinton told reporters in Washington. "I see it as building an ongoing partnership between two great nations that share a huge border and a common future, have some common problems, and inevitably some disagreements."
The major common problem is their 2,000-mile border, seen by poor Mexicans as a stepping stone to prosperity, from the Third World to the First. In August new US laws come into force that will, if not amended, mean that new arrivals who do not qualify for citizenship or do not want US citizenship will not be entitled to federal welfare benefits. These provisions are accompanied by a tougher approach to illegal immigration.
The legislation is not popular with some US states, which fear they could end up funding welfare programmes for legal immigrants. It worries the Mexican authorities, however, who fear that emigration - which provides an important safety valve for internal discontent and a reliable source of US dollars - could become even harder than at present.
Mr Zedillo will tell Mr Clinton the key is in helping narrow the economic gap, otherwise Mexicans will always head north.
Mr Clinton is expected to congratulate Mr Zedillo on his efforts to curb the flow of marijuana, cocaine and heroin across the border although the Mexican President's critics say many government officials at federal, state and local level are still in the pay of drug lords.
Last week Mexico announced it was scrapping its corruption-riddled anti- narcotics agency and giving its duties to the attorney-general's office. The head of the agency, an army general, was arrested in February for protecting the country's leading drug baron.
Mr Clinton and Mr Zedillo are expected to sign a vaguely-worded agreement on the security of US drug enforcement agents. The latter seek the formal right to carry weapons on Mexican soil for their own protection against violent drug trafficking gangs. Mexico has long opposed the idea, citing its sovereignty, but in effect most US agents carry weapons anyway.
In case it all seems one-way, Mexico will protest to the US over the influx of weapons. Mexico's ambassador to Washington, Jesus Silva Herzog, said Mexican drug gangs get most of their guns from the US because of lax gun laws and poor border checks.