There are packages that purport to make it easy to install Rtools, but I avoid these and setup my .Rprofile to point my PATH at the Rtools directory that I install manually.

https://cran.r-project.org/bin/windows/Rtools/

I have no idea why RStudio has such kind of problems from time to time but there is a manual work-around described here:

https://github.com/rwinlib/r-base/wiki/Testing-Packages-with-Experimental-R-Devel-Build-for-Windows

Basically you have to set two environment variables to point to the correct installation path of Rtools:

Sys.setenv(PATH = paste("C:/Rtools/bin", Sys.getenv("PATH"), sep=";"))
Sys.setenv(BINPREF = "C:/Rtools/mingw_$(WIN)/bin/")

Ensure that for the BINPREF path, the final slash is included after bin.

To avoid losing this change after restarting RStudio you could modify your (Windows) environment variables instead or add the following rows to your .Renviron file that is executed at each startup of R.

BTW: The $(WIN) part is no typo but required so that R can inject "32" or "64" depending on the R version you are using (32 or 64 bit).

Edit 1: See also this r-bloggers article published recently: https://www.r-bloggers.com/quirks-about-running-rcpp-on-windows-through-rstudio/

Turns out when I installed RTools I left out the R 2.15.x+ toolchain option in the installation, which lead to the gcc never being installed. Hopefully, this post will serve as a diagnostic guide if RStudio fails to register RTools.

Thank you everyone for your help.

The message indicates RTools isn't installed properly. Download and install it like so:

1. Go here
2. Download rtools for your version of R
3. Find the file that just downloaded
4. Double click on it to start installation
5. Close and reopen RStudio
6. Everything should work now!

A nice 2-minute video explainer can be found here.

Why is RTools necessary in the first place?

Rtools adds are some tools to allow you to build packages. Not all packages need it; just the ones that use C, C++ or Fortran code.

If you have problems installing

• If the instructions above don't result in a successful installation of Rtools, the following may help.
• Re-install R. Try to stick to the default installation settings if possible. Don't forget to close all current R sessions before reinstalling, then start a new R session and see if it works as expected. If not, try downloading and installing Rtools as outlined at the top of this answer; hopefully it installs as expected now.
• Make sure your anti-virus software isn't preventing it being installed. Anti virus software can sometimes mistake it for something harmful and quarantine it.
• When reinstalling R, or when installing Rtools manually, be careful to look for any indication that you do not have write permissions to the drive you're installing to. If you don't have permission to install certain things, that may be what's causing Rtools to not install correctly. This is more likely to happen if there are multiple users on your Windows computer, or if your organisation has strict policies about what can be installed. To look into this, figure out where Rtools is being installed to, and ensure you have the ability to write to that folder.

Rtools40 requires that you add its bin directory to your PATH variable. The full instructions are here.

You can update your ~/.Renviron file with any of the following methods:

You can do that manually by opening ~/.Renviron and putting the following in it:

PATH="${RTOOLS40_HOME}\usr\bin;${PATH}"

You can also use R (Gui or RStudio or Shell) with the following:

writeLines(
    'PATH="${RTOOLS40_HOME}\\usr\\bin;${PATH}"',
    con = file("~/.Renviron", open = "a")
)

Both of these methods require a restart of R.

After installation is complete, you need to perform one more step to be able to compile R packages: you need to put the location of the Rtools make utilities (bash, make, etc) on the PATH. The easiest way to do so is create a text file .Renviron in your Documents folder which contains the following line:

CopywriteLines('PATH="${RTOOLS40_HOME}\\usr\\bin;${PATH}"', con = "~/.Renviron")

Now restart R, and verify that make can be found, which should show the path to your Rtools installation.

CopySys.which("make")
## "C:\\rtools40\\usr\\bin\\make.exe"

https://cran.r-project.org/bin/windows/Rtools/

The second part with packages not being found has to do with upgrading the R version e.g. 3.5 to 3.6 or 3.6 to 4.0. If you go to Documents\R\win-library there will be a version folder with the libraries installed inside. Here is a script that will install the old libraries.

Copylib_loc <- "C:/Users/apdev/Documents/R/win-library/3.3"
to_install <- unname(installed.packages(lib.loc = lib_loc)[, "Package"])
to_install
install.packages(pkgs = to_install)

https://community.rstudio.com/t/reinstalling-packages-on-new-version-of-r/7670/4