Mr Jaspan, 42, currently editor of the Scotsman, replaces Jonathan Fenby who resigned last month after 18 months with the paper. According to a statement, he was the unanimous recommendation of the selection committee appointed by the trust.
Hugo Young, chairman of the trust, said Mr Jaspan had "all the qualities to be a fine editor of the Observer."
When the trust bought the Observer from Lonrho in 1993 the title's sales, then falling, stood at just over 500,000.
Circulation has steadily declined to around 470,000, despite a series of scoops, including the revelation that the British government had been engaged in secret talks with the IRA long before No 10 was prepared to admit the links that led to the Downing Street Declaration in December 1993. The paper has also continued to lose money.
When Peter Preston, editor-in-chief of the Observer and the Guardian, announced the changes last month, he told staff that he wanted the paper "to feel loved and cherished" and that this was to be achieved by "motoring forward".
Although a seven-day operation is not expected, the company has said that the changes would "maximise the use of editorial talent and resources available to the two newspapers" and that both would retain separate identities.
Many senior staff privately fear that Mr Jaspan's appointment is based on a reputation for being "a cost-cutter not afraid to shake things up" and have questioned his suitability for the post.
However, Mr Jaspan said: "I have one aim, namely to strive to reinforce the values and distinguised traditions of the Observer and help ensure it plays a vital role at the heart of British politics and society."
While critics at the Observer see him as an astute operator, rather than a true visionary, supporters praise an energetic, occasionally abrasive, manner which "makes things happen". They say he will not be weighed down by the intellectual baggage of the old Left that has appeared to inhibit the paper's attempts to reinvigorate itself and "leap forward a generation".
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