Without knowing what bike you have all I can do is recommend a bag which I have been using for the last few years and have been so happy with – the Topeak Trunk Bag DXP.
As for attaching this to your bike, Topeak loads to choose from – I personally like the removable MTX BeamRack which is very strong and light too.
I’ve used this combo on both my London to Paris and London to Amsterdam bike rides and can’t recommend them highly enough.