It sure seems to have been asked before (2003), and before (2002), or before (2005)
The last link actually suggest a javascript-based solution, but for a fixed (i.e. non fluid) solution.
It is consistent however, with other advices found
The only way to do that is to put the floated element somewhere in the middle of the text. It’s impossible to get it perfect all of the time.
Or this one:
It consists of floating a vertical “pusher” element (such as img, but it’s probably smarter to just use an empty div), then floating the desired object under it, using the clear property. The major problem with this method is you still have to know how many lines there are of text. It makes things MUCH easier though, and could definitely be coded with javascript, just need to change the height of the “pusher” to the height of the container minus the height of the float (assuming your container isn’t fixed/min height).
Anyway, as discussed in this thread, there is no easy solution…
Cletus mentions in the comments this thread from 2003, which states once again the fact it can not easily be achieved.
However, it does refer to this Eric Meyer’s article, which comes close to the effect you want to achieve.
By understanding how floats and the normal flow relate to each other, and understanding how clearing can be used to manipulate the normal flow around floats, authors can employ floats as a very powerful layout tool.
Because floats were not originally intended to be used for layout, some hacks may be necessary to make them behave as intended. This can involve floating elements that contain floats, “clearing” elements, or a combination of both.
Yet, Chadwick Meyer suggests in his answer a solution based on the :before CSS selector (variation of Leonard‘s answer).
It does work here.
Update Apr. 2021: Temani Afif suggests in his answer using exbox combined with a shape-outside.
But do check out the Backwards Compatibility of Flexbox, even though its support by all browsers is quite good.