The agreement is expected to help the company work with firms in Scotland to develop solutions that could help tackle key challenges facing oil and gas firms.
These include maximising the recovery of reserves from finds in the North Sea and increasing the efficiency of operations in the area.
The agreement forms part of a programme of initiatives that Scottish Enterprise hopes could unlock an additional £80 million research and development spending over the next five years.
It provides a big vote of confidence for the Scottish technology sector.
The head of Statoil's Technology Invest arm, Richard Erskine, said: "Statoil is always looking for new technologies to find more oil, increase production, or improve operational efficiency.
"Scotland has a strong tradition in developing new oil and gas technologies and we believe this partnership will enable us to more effectively work with small technology companies to commercialise and implement their ideas."
Statoil hopes to start production from the $7bn (£4bn) Mariner heavy oil field development off Shetland in 2017.
However, as heavy oil is harder to produce and refine than lighter crude, technology can have a huge impact on the economies of such developments.
Gunnar Breivik, head of Statoil's Aberdeen office, said: "We don't see the end of the North Sea for many, many years."
While Statoil delayed work on the giant Bressay heavy oil field off Shetland in November because of the hefty costs involved, Mr Breivik said it was making good progress with efforts to develop a cheaper scheme.
Lena Wilson, chief executive of Scottish Enterprise, said the agreement could lead to a very significant contribution to turnover growth and the internationalisation of Scotland based businesses.
The agency hopes the agreement with Statoil could form a model for partnerships with firms in other industries.
Ms Wilson said it wants to see more large companies demanding innovative solutions from the Scottish small and medium sized enterprise base.
Finance Minister John Swinney witnessed the signing of the agreement.
Describing Statoil as formidable, he said the agreement was "a landmark contribution to the way in which we encourage the flow of innovation and development in the Scottish economy".
Mr Swinney said it would be difficult to quantify the scale and impact of the activity that might result.
But he noted: "What's absolutely clear is the significant opportunity in the North Sea with the volumes still to be extracted."
He said the agreement should help efforts to maximise the recovery of North Sea reserves and to reduce costs.
Aberdeen oil services giant Wood Group yesterday noted the UK oil and gas sector's operating costs rose an estimated 15% last year.
Firms will be invited to respond to technology challenges advertised by Statoil. It will share information about favoured schemes with Scottish Enterprise, which may part-fund development work.
Scottish Enterprise expects ownership of the intellectual property developed by Scottish firms to remain with them.