Unfortunately you haven’t been very specific on your requirements. Since even the cheapest handheld DMM will be able to measure 10Mohm, the big question is: what resolution, what accuracy?
In general, accurate resistance measurement isn’t exactly trivial, and it gets increasingly difficult for higher values. Very few modern bench meters offer better than 100ppm one year accuracy for the lower resistance values up to 1Mohm and 400ppm for 10Mohm. Exceptions at an affordable price can be found in some ancient high end meters, which are usually what I think is called ‘boat anchors’ in the English speaking world - I would probably call them fitted kitchen appliances
Some options for the used market:
Solartron/Schlumberger 7150(plus) is a very nice looking compact meter which can be had for cheap due to its age, and its AC accuracy was outstanding back then so it can still compete today, but resistance measurement isn’t particularly good at 500ppm up to 20Mohm. It has some other shortcomings too, so I’d consider it a good choice for the occasional need for high precision, but not as an everyday bench meter.
Fluke 8840A and 8842A are very nice meters with excellent long term stability, often found at reasonable prices <400€, but with only 200000 counts and one has to be aware that they will only do true RMS AC measurements when option 09 is fitted. Display and UI are most convenient, but there are no bells and whistles like continuity check or even diode test.
Beyond that, the usual suspects come into play: Agilent 34401A, Keithley 2000 and 2015THD can sometimes be had at reasonable prices, and they all offer 1200000 counts together with state of the art accuracy specs.
If you want to buy new, I would like to mention:
Rigol DM3068, one of the very few modern DMM that maintains high input impedance up to 20V. Specs are pretty much the same as the before mentioned Agilent/Keithley devices, even though I would expect inferior long term stability. Functionality is a bit of a mixed bag, as it has some shiny features like histogram, but lacks others that might be more important at times.
My personal favourite is the Picotest M3500 (aka Keithley 2100), which is about the same price as a Rigol DM3068, but is pretty similar to an Agilent 34401 spec. and feature wise. It comes with a ready to go Excel plugin that makes external data logging through USB really easy, a feature that requires more effort with most older meters that only come with GPIB (if at all). Long term stability is quite good, but still expect it to drift out of spec some 2-3 years after initial purchase for the V and A ranges, whereas of all things the ohms measurement might go out of spec after only half a year. This is the downside of buying a new precision bench meter – you will need to re-calibrate the unit for at least the first three years…