Postgres.app setup: getting `which psql` to return desired path

I just installed Postgres.app, and now which psql returns nothing. I followed the instructions listed on the Postgres site; here's what I did:

1) Dragged my old version of Postgres to the trash. Emptied trash.

2) Downloaded the current version of Postgres.app. Dragged it to Applications folder.

3) Restarted Terminal.

The output I'm looking for from which psql is something like: /Applications/Postgres.app/Contents/Versions/9.3/bin/psql

When I run brew install postgresql followed by which psql, I get /usr/local/bin/psql. Which is at least something, but it's not what I want.

In case it's useful, here's my .bashrc:

if [ -f ~/.bash_profile ]; then
    source ~/.bash_profile
fi

PATH="/Applications/Postgres.app/Contents/MacOS/bin:$PATH"
export DYLD_LIBRARY_PATH="/Applications/Postgres.app/Contents/MacOS/lib:$DYLD_LIBRARY_PATH"

### Added by the Heroku Toolbelt
export PATH="/usr/local/heroku/bin:$PATH"

rvm get stable --auto-dotfiles

export PATH="$PATH:$HOME/.rvm/bin" # Add RVM to PATH for scripting

And my .bash_profile:

export PATH=/usr/local/bin:$PATH
export PATH=/usr/local/share/python:$PATH

# Python
export WORKON_HOME=$HOME/.virtualenvs
export VIRTUALENVWRAPPER_PYTHON=/usr/local/bin/python2.7
export VIRTUALENVWRAPPER_VIRTUALENV_ARGS='--no-site-packages'
export PIP_VIRTUALENV_BASE=$WORKON_HOME
export PIP_RESPECT_VIRTUALENV=true
if [[ -r /usr/local/share/python/virtualenvwrapper.sh ]]; then
    source /usr/local/share/python/virtualenvwrapper.sh
else
    echo "WARNING: Can't find virtualenvwrapper.sh"
fi

export PS1="\h:\w \u\$ "

# for git
LESS="-qrX -P %lt"
export LESS

# colorize shell output
export CLICOLOR=1
export LSCOLORS=Hxfxcxdxbxegedabagacad

#========== ALIASES ===========

alias u="cd .."
alias uu="cd ../.."
alias uuu="cd ../../.."
alias cd..="cd .."
alias rm="rm -i"
alias ll="ls -laFGh"
alias ls="ls -FGh"
alias new="ls -lat | head -15"

# node needs to not have DYLD_LIBRARY_PATH set
alias node="DYLD_LIBRARY_PATH=''; node"

# postgres stuff
PATH="/Applications/Postgres.app/Contents/MacOS/bin:$PATH"
export DYLD_LIBRARY_PATH="/Applications/Postgres.app/Contents/MacOS/lib:$DYLD_LIBRARY_PATH"

[[ -s "$HOME/.rvm/scripts/rvm" ]] && source "$HOME/.rvm/scripts/rvm" # Load RVM into a shell session *as a function*

Many thanks!