Agostinelli was born to Italian immigrant parents outside of Rochester, New York, and attended the Aquinas Institute. He obtained his BA from St. John Fisher College in 1976 and then attended Columbia University where he received his MBA, graduated with highest honours in 1981 and sits on the Alumni Board, He returns regularly to give speeches. Agostinelli is a certified public accountant.

Agostinelli began his career in financial services at the investment bank Jacob Rothschild in Switzerland from 1981 to 1982 and then joined Goldman Sachs and became a senior partner where he worked for five years and founded the firm's international mergers and acquisitions Business in London and then while at Lazard Freres he was involved in a number of the largest transactions in European takeover history. In 1995 Agostinelli and Steven Langman started their own firm, the Rhône Group.

He is a senior member of the Marine Corps Scholarship Foundation led by the American Patriots Campaign Cabinet, and a senior board Director on the American Italian Cancer Foundation. Agostinelli is on the board of Directors of the National Review Institute and the American Veterans Center Agostinelli is known for writing articles in the Wall Street Journal and The Washington Times on various political, economic and social issues. Agostinelli was listed in 1997 as a member of the Bilderberg Group.

Agostinelli is a friend of former French President Nicolas Sarkozy and former Spanish Prime Minister José María Aznar. In 2007 President Sarkozy admitted to Le Monde that Agostinelli, his wife and another family had paid the $60,000 per week fee on a luxury villa for him and his family during his 2006 holiday to the United States. Agostinelli has often been seen jogging with Sarkozy.

Agostinelli is a member of the Council on Foreign Relations and a leading supporter of Zionist and neoconservative causes. He is one of the Founding Members of the Friends of Israel Initiative. He is former Vice-Chairman of the Council for the United States and Italy (CONSIUSA), a member of the Investment Committee of Corporate World Opportunities of BSI Group and a Director and advisor to a number of European and U.S. philanthropic and civic institutions. In 2008 Agostinelli provided substantial funding to the presidential campaigns of John McCain and Rudy Giuliani.

A delegation of the Friends of Israel Initiative, which included Agostinelli, met with President Shimon Peres at Beit HaNassi in Jerusalem in July 2011. The delegation included former Spanish Prime Minister José Aznar, former US Ambassador to the United Nations John R. Bolton, and Nobel Peace Prize laureate Lord David Trimble. The President held a working meeting with the group and presented an overview of the situation in Israel and the region at large. Agostinelli stated: "Israel is a fundamentally important part of the Western world. It is a democracy under fire, and we must be resolute in defence of its legitimacy."

Agostinelli has four children and collects wine and art. Agostinelli counts Nicolas Sarkozy, George W. Bush, Jeb Bush and José María Aznar as close friends. While based between New York City and Palm Beach, he maintains additional homes in London and Paris, all of which are interior designed by Jacques Grange. In 2014 Agostinelli reportedly purchased the first landmarked estate in Palm Beach known as "La Loma" built by Gustav Maass and John Volk, which was on the market for $14.5 million through Sotheby's International Realty and sold for $12 million. According to the Sunday Times Rich List 2015, Agostinelli is 'building a home in Henley-on-Thames'. In 2017 The Sunday Times reported that Agostinelli recently spent £25 million on a home in South Kensington, London. He has also invested £60 million in WeWork.