Work to install the new surface began following a Green Day concert on 19 June and it will be tested for the first time when Chelsea and Manchester United clash in the Community Shield on 8 August.
STRI chief executive Gordon McKillop said: "STRI has worked with Wembley for thirteen months providing research and analysis of the playing performance of the pitch, advising on strategy and working on long-term objectives to enhance the quality of the playing performance. We have had many constructive and positive discussions with Wembley over the last few weeks on what would be the best way forward to make significant improvements to the pitch. In relation to this STRI presented an alternative strategy for 2010 to change the construction of the pitch, which Wembley agreed was the best way forward and is now proceeding with this."
He added: "We are pleased that Wembley has adopted our proposed strategy which should see improvements to the pitch during 2010. This new structure of pitch does not require the previous level of research and consultancy from the STRI team and, therefore, we feel it is the right time to resign. We wish the Wembley team every success with the new pitch and would welcome working with them again in the future."
A statement from the FA said there were no concerts scheduled at Wembley in the intervening period which would help the surface bed in.
But it confirmed that the stadium would continue to function as a multi use venue in order to generate revenue – widely believed to be the cause of the pitch problems.
Wembley National Stadium managing director Roger Maslin said: "The pitch is at the heart of the stadium and football is our number one priority. However, Wembley Stadium is a multi-use venue and developing our event calendar with a range of football, rugby, sports and entertainment events is key to the success of our business plan. The crucial balance for us is to maintain a good quality playing surface for football, while at the same time fulfilling our business plan commitments and maintaining our heritage as a multi-event venue."
The FA statement said: "The Desso pitch will be in place from June throughout the 2010-11 football seasons which concludes with the Football League Championship Final at Wembley. This will be followed by a full schedule of concerts in the summer of 2011. In 2012, Wembley will focus on the London 2012 Olympic and Paralympic Games, following that summer’s concert season.
"Should the FA be successful in its bid to host the 2018 FIFA World Cup, the pitch will be used entirely for football in that calendar year through until the completion of the tournament."Wembley Stadium remains committed to providing the best possible variety of world class sporting and other events, providing value for our Club Wembley members, who are fundamental to the success of the Stadium."