Weston began his career as a mechanical engineer with British Gas. He later became a consultant with the Boston Consulting Group and, following this, joined News International in 1995 where he worked as director of circulation and sales and head of business development.
Hinton said: "This is a time of exciting change for [Dow Jones] and Ian brings years of top-level experience in the newspaper industry.
"He has been key to developing radical change in News Corporation's British newspapers, in particular the company's recent $1.3bn project to install state-of-the-art printing presses."
News International, which publishes The Sun and The Times newspapers, will not be replacing Weston.
Weston said: "Dow Jones is a phenomenal company with great potential to grow and prosper in the years to come. I am honoured to be invited to play a part in making it happen."
Rupert Murdoch's News Corporation, owner of News International, finalised its $5.6bn (£2.8bn) takeover of Dow Jones & Co last week, after shareholders of the company voted to approve the deal.