The phrase "we have since learned" is correct and usable in written English.
You can use it to describe a situation in which you have obtained knowledge or information since a certain point in the past. For example: "We have since learned that there are more efficient ways of doing this task."
We have since learned that such deposits may not be allowed in rent-stabilized buildings.
As we have since learned, "La Bayadère" means more than "The Kingdom of the Shades".
We have since learned -- rather, relearned -- that urban life thrives on streets and sidewalks.
"We have since learned that we were misled about his conduct during his journey," The Sun writes in its clarification.
Home buyers seized on these opportunities to buy houses that they and we have since learned they could not afford.
"We have since learned that many people actually make good decisions, but they are based on inadequate information".
Sadly, we've since learned that Miss Leatha has passed away, leaving the legacy of her business (which she started with just $2 in 1976) to her family.
We've since learned that advertisers don't need depth — not when they can saturate so many advertising spaces and opportunities.
When I mentioned what I had in mind, she said: "Brilliant – when do we start?" That was two years ago, and we've since learned a lot about what works - and what doesn't.
Though many Muslims Americans like me kept quiet in the years after 9/11 for fear of arousing illegitimate government suspicion, we've since learned that it is not silence that will keep the government from overstepping its bounds.
While Live Another Day proved a financial success, we've since learned the next 24 mini-series won't feature Jack Bauer, which might turn out to be a continuation too far.
