Mr Barnier's new job will include supervision of the City of London
France will take charge of the key internal market post in the new 27-strong European Commission, whose composition has just been announced.
Former French agriculture minister Michel Barnier got the job.
The UK's representative is the new EU foreign policy chief, Baroness Ashton. She will be a vice-president of the commission.
The nominations will not be confirmed until they are approved by the European Parliament at hearings in January.
Commissioners staying on
Joaquin Almunia from Spain will become EU Competition Commissioner - another much-coveted post in the EU's executive arm. He will also be a vice-president, like Lady Ashton.
Olli Rehn from Finland will be Economic and Monetary Affairs Commissioner, replacing Mr Almunia in that post. He was previously EU Enlargement Commissioner.
With his internal market job Mr Barnier will control supervision of the EU market for financial services, most of which is in the City of London.
Timothy Kirkhope MEP, the UK Conservative leader in Brussels, said that "the loss of an Anglo-Saxon voice in the commission's top economic team is of concern, given the recent spate of over-prescriptive economic and financial legislation to come from Brussels".
Karel De Gucht from Belgium will be Trade Commissioner, Commission president Jose Manuel Barroso said. Mr De Gucht currently heads the EU development and humanitarian aid directorate.
The commission is responsible for drafting EU legislation and acts as guardian of the EU treaties. The appointments are for five years and each member state has a commissioner.
Fourteen of the 27, including Mr Barroso, were in the outgoing commission.
Tackling economic woes
Announcing the new line-up, Mr Barroso said the commission would face huge challenges in getting the world's biggest trading bloc out of the economic crisis.
Mr Almunia will head EU competition - one of the top economy jobs
Mr Barroso has included nine women in his team - one more than in the outgoing commission. They include Danish Environment Minister Connie Hedegaard, who will take up a new post - that of Climate Action Commissioner.
A Czech politician, Stefan Fuele, will take charge of the EU's enlargement job. He will also be in charge of the EU's neighbourhood policy concerning Ukraine and other former Soviet states.
Germany's Guenther Oettinger was named Energy Commissioner, a reflection of the policy's growing importance for the EU, the BBC's Oana Lungescu reports from Brussels.
The biggest countries in Eastern Europe also got plum jobs - budget for Janusz Lewandowski from Poland and agriculture for Romania's Dacian Ciolos.
Three new portfolios have been created: Climate Action; Home Affairs; and Justice, Fundamental Rights and Citizenship.
The commissioners are drawn from the main European political groupings: the European People's Party (EPP - centre right), the Progressive Alliance of Socialists and Democrats (S&D - centre-left) and the European Liberal Democrat and Reform Party (ELDR).
Here is the new commission line-up, with nationalities and political allegiance:
President - Jose Manuel Barroso (Portugal - EPP)
High Representative for Foreign Affairs and Security - Lady Ashton (UK - S&D)
Competition - Joaquin Almunia (Spain - S&D)
Economic and Monetary Affairs - Olli Rehn (Finland - ELDR)
Internal Market and Services - Michel Barnier (France - EPP)
Trade - Karel De Gucht (Belgium - ELDR)
Energy - Guenther Oettinger (Germany - EPP)
Environment - Janez Potocnik (Slovenia - ELDR)
Employment, Social Affairs and Inclusion - Laszlo Andor (Hungary - S&D)
Budget - Janusz Lewandowski (Poland - EPP)
Enlargement - Stefan Fuele (Czech Republic - S&D)
Justice, Fundamental Rights and Citizenship - Viviane Reding (Luxembourg - EPP)
Maritime Affairs and Fisheries - Maria Damanaki (Greece - S&D)
Regional Policy - Johannes Hahn (Austria - EPP)
Climate Action - Connie Hedegaard (Denmark - EPP)
Research and Innovation - Maire Geoghegan-Quinn (Republic of Ireland - ELDR)
Transport - Siim Kallas (Estonia - ELDR)
Health and Consumer Policy - John Dalli (Malta - EPP)
Agriculture and Rural Development - Dacian Ciolos (Romania - EPP)
International Co-operation, Humanitarian Aid and Crisis Response - Rumiana Jeleva (Bulgaria - EPP)
Digital Agenda - Neelie Kroes (the Netherlands - ELDR)
Development - Andris Piebalgs (Latvia - EPP)
Home Affairs - Cecilia Malmstroem (Sweden - ELDR)
Industry and Entrepreneurship - Antonio Tajani (Italy - EPP)
Taxation and Customs Union, Audit and Anti-Fraud - Algirdas Semeta (Lithuania - EPP)
Inter-Institutional Relations and Administration - Maros Sefcovic (Slovakia - S&D)
Education, Culture, Multilingualism and Youth - Androulla Vassiliou (Cyprus - ELDR)