Thomson last month became the first non-Briton to edit the Times. Barber will take over his role as managing editor of its US edition in May.
In his new role, Barber will be responsible for the US edition of the FT as well as overseeing all aspects of the US print and online editorial operations.
Andrew Gowers, editor of the Financial Times in the UK, said: "I am delighted to appoint Lionel as the FT's US managing editor. He has achieved significant circulation growth for the FT's continental European edition for the last two years, and I am certain that he is the right man to take us into the next phase of the FT's expansion in the US."
The FT has made several other appointments at its US office, including the new position of US news editor, which goes to David Wighton, the current financial news editor.
The appointments bring the number of journalists on the paper's US editorial team to 70, working in eight US cities. The newspaper has more than quadrupled its circulation in the last four years to 142,000 from 37,000 in 1997.
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