There is no clear answer to this, and probably never will be. If you're looking for an official word on what's canon and what isn't, or perhaps even levels of canon as there are in Star Wars, you'll not find anything like that with Asimov's works. And as you'll see, this may have been left deliberately open to interpretation.
Also, this isn't a case of a large franchise with someone passing down edicts, it's a different situation entirely. Asimov's works can almost certainly be considered canon, but there's really very little guidance after that. But we can apply reason:
The stories in the multiple-author anthology "Foundation's Friends" were written while Asimov was alive, but are of questionable "canon". Some of the stories set in the Robot/Foundation/Empire universe even contradict Asimov's stories. The tone of much of this book seems to be one of affectionate pastiche more than an attempt to add to Asimov's body of work. Similarly, the Robot City books (which I haven't read) appear to be more of an attempt to riff off of the concept of Asimov's robots.
Roger MacBride Allen's trilogy of books about the robot Caliban is a bit of a special case: The good doctor approved outlines for these books before he died, so an argument could be made for including them in the Asimov canon. Additional books by Mark W. Tiedemann and Mickey Zucker Reichert were approved by Asimov's estate, but Asimov himself had nothing to do with these. The "Second Foundation Trilogy" by Greg Bear, Gregory Benford, and David Brin was also authorized by his estate, but the series was conceived after Asimov's death.
Asimov himself was fond of linking his works together, but left gaps in what was "official". The books Nemesis and The End of Eternity may or may not be linked to the Robot/Empire/Foundation books - and the author was tantalizingly ambiguous about their status.
He also clearly had no issues with others extending his work; Robert Silverberg wrote three novels that were expansions of Asimov stories.
Asimov's fiction was also a small part of his output; he wrote many non-fiction books, and was particularly passionate about his volumes popularizing science. Education was clearly important to him. He was also very supportive of new writers - he wrote several essays on how he became a published author, with advice for others on the same path - and he considered intelligence and imagination to be of paramount importance.
A lack of any official body to set canon means that readers are free to determine the canonicity of these works on their own. It seems to me that this is exactly the way Asimov would have wanted this: Readers using their imaginations to decide on canon.