Rosenmöller was born into an upper class family, his father being CEO of Vroom and Dreesman. After finishing atheneum-b in Haarlem in 1974, Rosenmöller studied sociology. During his study Rosenmöller became associated with radical socialist, maoist groups. He was a member of Group of Marxist-Leninists/Red Dawn. He stopped studying in 1978 to work in the harbour of Rotterdam. He intended to work together with and electrify the masses. He works as for the shipping company Müller Thomson. In 1985 he became a member of the board of the Transportation branch of the Rotterdam FNV labour union. He negotiated with VNO-NCW and is spokesperson during several strikes. Rosenmöller got national fame because of his radical position in these negotiations and strikes.
In 1989, he became member of the newly founded party GroenLinks. GroenLinks was formed by four other parties, but Rosenmöller joined as an independent. In the 1989 election, he was the sixth on the list of the GroenLinks and the first independent; he was narrowly elected into the lower house of parliament. In 1993 he was candidate party leader together with Leonie Sipkes, but they lost the internal elections to Mohammed Rabbae and Ina Brouwer. After the defeat of the GroenLinks in the 1994 election, Rosenmöller became the party leader.
As party leader he was the unofficial leader of the opposition against the first and second cabinets of Wim Kok, as the much larger opposition party CDA was not functioning well as an opposition party. Rosenmöller led GroenLinks in the successful 1998 election. In 2002, however, the political climate had changed. Rosenmöller participated in the opposition against the rise of Pim Fortuyn. At a party congress, he described Fortuyn as "extremely right-wing." He lost the disastrous 2002 elections. In the hardened political climate after the murder of Fortuyn, serious threats against Rosenmöller's life and family were made. Because of this, Rosenmöller left politics. His successor as leader of the GroenLinks party was Femke Halsema.
In 2003, after leaving politics, Rosenmöller became journalist for the IKON, a minor broadcasting organisation. He also chairs PAVEM, a government advisory committee on the position of migrant women, in which Princess Máxima has a seat.
- Rosenmöller has five children.nl:Paul Rosenmöller