How about the term, "Pencilpusher" ?
Not specifically for computer-users, but more for suitable for someone like you described as "an accountant or any other person who works in the office and spends most of the day in front of computer screen."
pencil-pusher noun N. Amer. informal
another term for pen-pusher.
No way he was going to let those pencil pushers from accounting pity him.
a person with a clerical job involving a lot of tedious and repetitive paperwork.
Or the term "Hacker" ?
This could be suitable for programmers, code-writers, computer professionals etc.
hacker |ˈhakə| noun informal
1 a person who uses computers to gain unauthorized access to data.
2 an enthusiastic and skilful computer programmer or user.
hack |hak| verb
gain unauthorized access to data in a system or computer:
[ no obj. ]
They hacked into the bank's computer.
[ with obj. ]
Someone hacked his computer from another location.
hack |hak| noun informal
1 an act of computer hacking.
The challenge of the hack itself.
2 a piece of computer code providing a quick or inelegant solution to a particular problem:
This hack doesn't work on machines that have a firewall.
hacking adjective, mass noun
Outlawing hacking has not stopped it.
If you're more concerned with implying the connotation of extended visual contact with computers, monitors, video-screens etc. You could make a reference to having "Square-eyes" ?
square eyes plural, noun Brit. humorous
eyes supposedly affected by excessive television viewing:
He watched so much TV he'd got square eyes.