redirect COPY of stdout to log file from within bash script itself

#!/usr/bin/env bash

# Redirect stdout ( > ) into a named pipe ( >() ) running "tee"
exec > >(tee -i logfile.txt)

# Without this, only stdout would be captured - i.e. your
# log file would not contain any error messages.
# SEE (and upvote) the answer by Adam Spiers, which keeps STDERR
# as a separate stream - I did not want to steal from him by simply
# adding his answer to mine.
exec 2>&1

echo "foo"
echo "bar" >&2

Note that this is bash, not sh. If you invoke the script with sh myscript.sh, you will get an error along the lines of syntax error near unexpected token '>'.

If you are working with signal traps, you might want to use the tee -i option to avoid disruption of the output if a signal occurs. (Thanks to JamesThomasMoon1979 for the comment.)

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Tools that change their output depending on whether they write to a pipe or a terminal (ls using colors and columnized output, for example) will detect the above construct as meaning that they output to a pipe.

There are options to enforce the colorizing / columnizing (e.g. ls -C --color=always). Note that this will result in the color codes being written to the logfile as well, making it less readable.

Solution for busybox, macOS bash, and non-bash shells

The accepted answer is certainly the best choice for bash. I'm working in a Busybox environment without access to bash, and it does not understand the exec > >(tee log.txt) syntax. It also does not do exec >$PIPE properly, trying to create an ordinary file with the same name as the named pipe, which fails and hangs.

Hopefully this would be useful to someone else who doesn't have bash.

Also, for anyone using a named pipe, it is safe to rm $PIPE, because that unlinks the pipe from the VFS, but the processes that use it still maintain a reference count on it until they are finished.

Note the use of $* is not necessarily safe.

#!/bin/sh

if [ "$SELF_LOGGING" != "1" ]
then
    # The parent process will enter this branch and set up logging

    # Create a named piped for logging the child's output
    PIPE=tmp.fifo
    mkfifo $PIPE

    # Launch the child process with stdout redirected to the named pipe
    SELF_LOGGING=1 sh $0 $* >$PIPE &

    # Save PID of child process
    PID=$!

    # Launch tee in a separate process
    tee logfile <$PIPE &

    # Unlink $PIPE because the parent process no longer needs it
    rm $PIPE    

    # Wait for child process, which is running the rest of this script
    wait $PID

    # Return the error code from the child process
    exit $?
fi

# The rest of the script goes here

The accepted answer does not preserve STDERR as a separate file descriptor. That means

./script.sh >/dev/null

will not output bar to the terminal, only to the logfile, and

./script.sh 2>/dev/null

will output both foo and bar to the terminal. Clearly that's not the behaviour a normal user is likely to expect. This can be fixed by using two separate tee processes both appending to the same log file:

#!/bin/bash

# See (and upvote) the comment by JamesThomasMoon1979 
# explaining the use of the -i option to tee.
exec >  >(tee -ia foo.log)
exec 2> >(tee -ia foo.log >&2)

echo "foo"
echo "bar" >&2

(Note that the above does not initially truncate the log file - if you want that behaviour you should add

>foo.log

to the top of the script.)

The POSIX.1-2008 specification of tee(1) requires that output is unbuffered, i.e. not even line-buffered, so in this case it is possible that STDOUT and STDERR could end up on the same line of foo.log; however that could also happen on the terminal, so the log file will be a faithful reflection of what could be seen on the terminal, if not an exact mirror of it. If you want the STDOUT lines cleanly separated from the STDERR lines, consider using two log files, possibly with date stamp prefixes on each line to allow chronological reassembly later on.