Thapar, who was unavailable for comment, is currently freelancing on the Evening Standard City desk.
Editor-in-chief Neil told PRWeek: 'It is a difficult role to fill. We needed someone with an international dimension. There are stories breaking in Spain, Italy, France and other countries.'
Thapar was investment editor at The Mail on Sunday for five years, until becoming City editor of online news service ShareCast in 2000.
This year he has worked as a UK equities consultant for a City firm.
Pfeifer's coverage of banking, fund management and the pharmaceutical industry was well respected. Thapar will be expected to add to that, said deputy editor Ian Watson. 'He's been around a long time,' said Watson.
'We have to look at the world as a whole, and Europe is what we are mainly concentrating on. People are expecting us to be ahead of the game.'
Watson said he also wanted more coverage of Asian markets: 'We have not concentrated on that up to now but, as the world economy recovers, Asia is growing in importance. We ignore it at our peril.
'At present, we don't do face-to-face interviews. We should start doing some.'
Neil said there were no immediate plans to add new sections to the paper.
'Editorially, we will expand as the money comes in,' he said. 'We are keeping it a single-section read for very busy people.'
Last month, 94,000 copies of The Business were given away free with The Mail on Sunday in London, in an arrangement that saw circulation almost double to 207,400.
Earlier this year, Neil admitted the title's previous incarnation as Sunday Business had failed to compete with rivals. Its 2002 relaunch as The Business saw it take on an international agenda, similar to The Wall Street Journal and the Financial Times.