It follows a $2.6bn (£1.6bn) contract for its engines from the airline in October 2012. John Forkin of Marketing Derby said the deal was a major boost to the city's global reputation.
The latest order is to power 50 Boeing 787 Dreamliner aircraft with Trent 1000 engines.
Thirty of the Boeing aircraft will be operated by Singapore Airlines, with the airline's subsidiary, Scoot, taking the other 20.
Eric Schulz, president of civil large engines at Rolls-Royce, said: "We are very proud that Singapore Airlines, one of the most respected carriers in the world, and its subsidiary Scoot have placed their trust in our Trent 1000 and our ability to deliver superior product and service performance.
"This decision is a tremendous reflection of the deep relationship that Rolls-Royce and Singapore Airlines enjoy, and allows us to continue to develop our strategic alignment."
Singapore Airlines and Scoot currently operate a total of 88 Rolls-Royce-powered aircraft, with 88 more on order.
Jonathan Asherson, regional director in South East Asia for Rolls-Royce, added: "This decision for Trent 1000 engines underpins the strong partnerships we have developed with Singapore over many years.
"Singapore Airlines, and SIA Engineering Company, have been core components of our strategic relationships here that now include major services and manufacturing activity, technology acquisition and training. We are committed to further developing these successful partnerships."
The Singapore Airlines order for the Boeing 787-10X is conditional on Boeing formally launching the programme.
At the end of May (2013), Singapore revealed its intention to order 30 additional Airbus A350-900 aircraft, which will all be powered by the Trent engines.
John Forkin of Marketing Derby said: "The Dreamliner deal alone is valued at $4bn and is testament to the quality of the workforce in design, engineering, production and sales.
"The city is home to the UK's leading clusters in aerospace, rail and nuclear technology and central to this is a quality workforce centred on advanced engineering.
"Up-and-coming developments such as the Global Technology Campus on the city's south side, and the University Technology College on Pride Park, as well as the Rolls-Royce academy itself, will play an important role in keeping Derby globally competitive and attractive for investors."
The Dreamliner deal means the Rolls-Royce order book now stands close to £70bn and the company now employs 45,000 staff across the world, with 13,000 in Derby.