Configure Logrotate

/etc/logrotate.conf 

/etc/logrotate.d/ufw   --> /var/log/ufw.log

# see "man logrotate" for details

# rotate log files weekly

weekly

# keep 4 weeks worth of backlogs

rotate 4

# create new (empty) log files after rotating old ones

create

# use date as a suffix of the rotated file

#dateext

# uncomment this if you want your log files compressed

#compress

# packages drop log rotation information into this directory

include /etc/logrotate.d

# system-specific logs may be also be configured here.

/var/log/ufw.log

{

        rotate 4

        weekly

        missingok

        notifempty

        compress

        delaycompress

        sharedscripts

        postrotate

                invoke-rc.d rsyslog rotate >/dev/null 2>&1 || true

        endscript

}