How can I put the current running linux process in background? [closed]

Suspend the process with CTRL+Z then use the command bg to resume it in background. For example:

sleep 60^Z  #Suspend character shown after hitting CTRL+Z[1]+  Stopped  sleep 60  #Message showing stopped process infobg  #Resume current job (last job stopped)

More about job control and bg usage in bash manual page:

JOB CONTROL
Typing the suspend character (typically ^Z, Control-Z) while a process is running causes that process to be stopped and returns control to bash. [...] The user may then manipulate the state of this job, using the bg command to continue it in the background, [...]. A ^Z takes effect immediately, and has the additional side effect of causing pending output and typeahead to be discarded.

bg [jobspec ...]
Resume each suspended job jobspec in the background, as if it had been started with &. If jobspec is not present, the shell's notion of the current job is used.

EDIT

To start a process where you can even kill the terminal and it still carries on running

nohup [command] [-args] > [filename] 2>&1 &

e.g.

nohup /home/edheal/myprog -arg1 -arg2 > /home/edheal/output.txt 2>&1 &

To just ignore the output (not very wise) change the filename to /dev/null

To get the error message set to a different file change the &1 to a filename.

In addition: You can use the jobs command to see an indexed list of those backgrounded processes. And you can kill a backgrounded process by running kill %1 or kill %2 with the number being the index of the process.