Khan is to meet Canadian prime minister Justin Trudeau in Montreal before travelling to Chicago and New York in a bid to promote London as a "key destination for investment, business and tourism", the mayor's office said.
He will also stress the importance of "building bridges rather than walls" - a reference to US presidential candidate Donald Trump's proposal to build a wall along the US-Mexico border.
Khan was involved in a spat with Mr Trump earlier this year over the Republican's call for a temporary ban on Muslims entering the US. The mayor criticised Mr Trump's "ignorant" view of Islam, with the billionaire tycoon responding by calling Mr Khan's remarks "rude" and "nasty."
Ahead of the trip, Khan said: "In the wake of Brexit it is hugely important that we strengthen London's ties with other major cities. The key theme I will take into every meeting on this visit is that London is and always will remain open for business."
The London mayor will join the Canadian PM as they address a global progress summit in Montreal, before meeting the city's mayor Denis Coderre and senior figures from Bombardier Business Aircraft, which is investing in London's Biggin Hill Airport.
He will then travel to Chicago where he will deliver a keynote speech to the Chicago Council for Global Affairs. He will also meet Shahid Khan, the owner of Fulham FC and NFL team Jacksonville Jaguars, to discuss investment in London.
In New York, the mayor will be introduced to Major League Baseball commissioner, Rob Manfred, to discuss plans to bring games to London and throw the first pitch at a New York Mets game.
He will also visit the Clinton Global Initiative during its annual meeting, where he is expected be joined on stage by Chelsea Clinton.
Khan will meet New York mayor Bill de Blasio and visit the New York Stock Exchange where he will join businesswomen to ring the closing bell.
During his trip, the mayor will be joined by 30 of London's fastest growing technology start-up businesses.
London's deputy mayor for business, Rajesh Agrawal, is leading the companies on a trade mission in a bid to secure new investment and discuss exporting to American markets.