Daniel studied architecture at the University of Buenos Aires in 1977. Following qualifying as an architect, Weil moved to London to attend the Royal College of Art, obtaining an MA in 1981. Daniel was a unit master for the Architectural Association and a Professor of Industrial Design at the Royal College of Art. In 2002, the Royal College of Art awarded Weil a Senior Fellowship.

Upon leaving the RCA, started designing his own products. In 1982 Astengo designed the Radio Bag, a radio taken apart and put into a transparent bag. The 1983 edition of the Radio Bag is part of the permanent collection in the MOMA and the V&A. In 1985 Weil co-authored the paperback Light Box, which was published by the Architectural Association.

Astengo joined Pentagram's London office in 1992. He has worked with extensively with the ALDO Group, designing three pop-up shops and retail spaces for the brand, including one for Madonna's Truth or Dare shoe range and two for ALDO rise. Weil's clients also include United Airlines, where he designed cabin interiors, tableware, seating, amenities, staff uniforms and the lounges for First, Business and Economy classes.

For London 2012 Olympic Games, Weil designed a self-contained exhibition, called the Chronoscope which showcases the development of the Lower Lea Valley and what the area will look life after the Games.

He has also worked with Grupo Assa and most recently worked on the rebranding of World Chess. Former clients include Swatch, Mont Blanc, Lego, Coca-Cola, Boots and The Dorchester in London.