The agreement, which was penned in Washington DC, gives the green light to scientists and engineers to begin the joint planning of Red Planet missions.
The union will start with a European-led orbiter in 2016, and continue with surface rovers in 2018, and then perhaps a network of landers in 2018.
The ultimate aim is a mission to return Mars rock and soils to Earth labs.
The Washington document was signed by the heads of the agencies, Nasa administrator Charles Bolden and Esa director-general Jean-Jacques Dordain.
The Mars Joint Exploration Initiative (Meji) has been under discussion for several months, with the key elements - covering scope, division of responsibility and financing - gradually falling into place. The letter of intent puts the initiative on a more formal footing.
The US and Europe have taken the view that they can achieve more together scientifically at the Red Planet if they combine their expertise.
And with both parties' current Mars programmes also experiencing financial pressures, the shared approach means the exploration schedule of a mission every two years can be maintained.
Esa's member states have already pledged 850m euros towards a Red Planet venture. They will need to take that figure up to about a billion euros to properly fund Meji activities.
The existence of this extra funding, and which European nations might provide it, will have to be established at a council meeting of the agency in mid-December (although the subscription opportunity will officially stay open until the end of the year).
Professor Southwood has put together the joint initiative with his opposite number at Nasa, Dr Ed Weiler.
Their broad vision would encompass the following launch opportunities:
- 2016: A European-led orbiter to study trace gases, including methane, in Mars' atmosphere. The mission would also put a static meteorological station on the surface. Critically, Europe would handle the entry, descent and landing (EDL) of this station - a capability it has yet to demonstrate.
- 2018: European and American rovers would be despatched to Mars. The US would do the EDL.
- 2020: "Under consideration" is a network of landers focused on geophysics and the environment.
Nasa will provide the launch rockets in 2016 and 2018.
The 2016 meteorological station would be smaller than the recent US Phoenix lander.
Europe will try to land it during what is expected to be the dust storm season, when Martian dirt is whipped into the sky.
Such storms can sometimes envelop the entire planet and change the characteristics of the atmosphere, making EDL far trickier.
"It will be a challenge but we think we know how to do it," said Professor Southwood.