I have seen this written many times on bus timetables etc.
and find no reason why someone wouldn't understand it.
To be extra clear, I would make one amend:: The train departs at 16 minutes past every hour.
Or even better
The train departs at 16 minutes past the hour, every hour.
ell.stackexchange.com/users/95928/Bee
What alephzero said (in comment) is also true of US English: "every hour at 16 past the hour."
From Merriam Webster dictionary Definition of past the hour used with a certain number of minutes to indicate how long after the beginning of an hour something will happen "
Trains leave every hour at ten minutes past the hour."
This is more colloquial, to my ear, than "past every hour" and Google agrees One can also say "16 minutes before the hour," whereas "before every hour" is almost unattested
ell.stackexchange.com/users/104056/Scott
You may hear more casual variations of this such as: There are trains at 16 past, every hour.
The trains are at 16 past, every hour.
Generally, the trains will not be running on the same schedule for the entire day, so you'll often hear this with a time constraint:
There are trains at 16 and 39 past, every hour, until 5.
There are trains at 16 and 39 past, every hour, from 9 until 5.
You'd also be likely to hear these further condensed: There are trains at 16 and 39 past until 5.
There are trains at 16 and 39 past from 9 until 5.
ell.stackexchange.com/users/103986/Chris Mack
The idiomatic expression in English related to this is "every hour, on the hour" (with the comma sometimes being omitted, as in: By 2002, the RUC was run every hour, on the hour , producing 12-hour forecasts with a 1 hour temporal resolution.
Which means that it ran at 10:00, 11:00, 12:00, etc etc.
Closely-related is "every hour, on the half-hour" (with the comma and/or the hyphen sometimes omitted,) as in: Retrieval times are 9:30, then every hour on the half hour , with the last retrieval at 3:30 (4:30 on Tuesday and Thursday).
To further approach your specific question, we also have "every hour on the quarter-hour", which I hope you might guess is: Train: Oxford Road to Urmston though it's only every hour, on the quarter hour , so not necessarily the best way.
All of that has been generalized to "every hour, on the X", where X is some number, and usually pluralized:
It looks like the buses leave every hour on the 16s .
This can also be generalized to frequencies other than hourly: Providing you with up to the minute breaking news, headlines and video, as well as traffic and weather updates every ten minutes on the ones .
This is, I think, a bit less-formal than some of the other correct expressions listed in other answers, but I would expect any competent English speaker to readily-grasp the meaning.
ell.stackexchange.com/users/104103/Roger
In British English (and I believe AmEng too)
there are idiomatic ways of stating specific times on the clock, although these expressions do not necessarily apply when speaking about hours and minutes in general.
You can write any time numerically in 12, or 24-hour format:
Trains depart at 15:16, 15:46.
16:16 etc
How we say those times depends on the number of minutes past the hour, and if writing them in words, we would write them as they should be spoken.
We don't usually use the words "hours" and "minutes" when quoting a specific time, and when the minutes are divisible by 5, for example: Five past four (16:05) Twenty-five past five (17:25) Twenty to six (17:40)
Also, when the time is precisely 15, 30, or 45 minutes past the hour, we tend to say: A quarter past five.
(17:15) Half-past five (17:30)
A quarter to six (17:45)
However, when the number of minutes is not divisible by 5, we do include the word "minutes", for example: Six minutes past four (16:06) In everyday situations, British English speakers tend to round times like this and say things like "It's nearly ten past four", or "It's just gone five past four".
Obviously that would not be the case with a transport timetable.
For the reasons above, we would definitely include the word "minutes" in your example, if only because it is an "unrounded" number of minutes (not divisible by 5):
The train departs at 16 minutes past every hour.
OR The train departs at 16 minutes past each hour.
It is also idiomatic, when speaking about any hour, to say "past the hour", as in this example from MW dictionary: Trains leave every hour at ten minutes past the hour.
ell.stackexchange.com/users/66325/Astralbee
In German, we can say  "jede Stunde um 16 nach" . I just overheard someone teaching there was no such possibility in English. Yet I found  "hourly at 45 minutes past"  in one answer  here . Is the following also correct?   The train departs at 16 past every hour.
Can I say: “The train departs at 16 past every hour“?
ell.stackexchange.com
<phrase-request><phrase-choice><time>
ell.stackexchange.com/questions/228889
ell.stackexchange.com/users/55131/Ludi
 The train departs at 16  minutes  past every hour.    The expression is correct in English and other variations are possible.
The expression is correct in English and other variations are possible.