The CleanSpace app provides users with details of the local air quality, which Lord Drayson hopes will raise awareness of the problem.
The app also rewards it users with CleanMiles for low emission journeys.
Last year, a Commons select committee report described air pollution as a “public health crisis”.
MPs on the Environmental Audit Committee called for new schools, care homes and hospitals to be built far away from major roads because of the dangers of air pollution.
It is estimated that it is responsible for 29,000 deaths in the UK each year.
Despite the government arguing that it was investing heavily to improve air quality, the UK Supreme Court ruled that ministers had to take immediate action to cut air pollution.
Lord Drayson, a Labour government minister between 2005 and 2010, said the idea for the CleanSpace app came from people asking what they could do to tackle global problems like climate change and air pollution.
“After coming out of government and deciding to start a technology business it really struck us that we are living at a time where modern internet technology gives us the tools to answer that question for people by giving them information about the air that they are breathing and motivating them to see the central truth, which is that the little things do add up,” he said.
“That is the core idea behind it. For us, it is not just telling people about the problem but motivating them to see that the solution is in all of our hands.”
The app, developed by Lord Drayson’s company, provides the user with a map and information about the air quality in the local area.
“The second aspect is that as you go about your day, the app automatically tracks you. We use the sensors within the phone to generate a signature of the way that you are moving so the phone can automatically work out how you are moving so it can work out whether you are walking, or cycling or in a vehicle,” Lord Drayson told BBC News.
If you are moving in a way that is not contributing to air pollution – cycling or walking – it credits you with what we call CleanMiles. Over time, you will be able to see what proportion of your journeys you are doing are clean or not clean.”
Lord Drayson said he hoped the app would raise people’s awareness that air quality changed all the time and that “you can make a difference to the air that you are breathing by choosing how you travel”.
He added that another key component of the app was to create an online community for like-minded people. “We know about the power of social networks and what we are trying to do is to create a social network to make a big change,” he added.
“We also know that there are people who are not aware of air pollution. What we found from our research is that by making people more aware then they start to think about this and this does change behaviour.”
In the future, the team behind the CleanSpace app plan to provide users with personal air quality monitoring devices in order to collect data that will be fed into the system.
“This will allow you to get information that is not just based on the aggregated data gathered by sensors around cities, it is the air quality you are breathing as you are moving,” Lord Drayson explained.
In June 2013, He broke the world land speed record for a lightweight electric car, hitting a speed of 204.2mph (328.6km/h).
Rather than motorsport being part of the problem, he said that he saw racing as an opportunity to “pioneer and showcase environmentally sustainable technology”.
“I helped found the Formula E motorsport championship, which has been a real success. I developed a very high performance race car to really showcase what electric cars could do,” he explained.
“What I have learned through racing and politics is that it is really important with issues like climate change and air pollution is to show people that the future can be better, but fun and exciting as well.”