Have a look at the LDWA website. They have a searchable database for paths in the uk, and you can display results as a map.
The routes up the west are limited, the best one has been mentioned with the Annandale Way, Clyde Walkway - there is quite a gap to fill in though.
An alternative may be Pennine Way, St Cuthberts Way, Borders Abbeys Way (via Hawick), then the Cross Border Drove Road to the Pentland Hills, Water of Lieth Walkway then picking up the John Muir Way. Follow the F&C canal to Glasgow.