How to paste values between two dataframes when conditions are respected

I have a large dataframe (my_DF) with 4 important columns: ID (1-->100), YEAR (2000, 2001, 2002, 2003, 2004, 2005), MONTH (January --> December), LENGHT (continuous values from 0.1 to 1.0). A thing like:

        YEAR      MONTH       ID   LENGHT 
1       2000     january      S1   0.2 
2       2000     january      S1   0.3
3       2000     january      S1   0.1 
4       2000     january      S2   0.5
5       2000     january      S2   0.3 
6       2000     february     S1   0.9
7       2000     february     S1   0.4 
8       2000     february     S1   0.6 
9       2000     february     S3   0.4
10      2000     february     S3   0.3 
11      2000     march        S1   0.7 
...

I need to add a new column to the dataframe, filled with the median lenght for each unique situation, so for each ID, YEAR and MONTH values.

I succeded in obtain the values I was looking for, thanks to aggregate:

agg <- aggregate(my_DF["LENGHT"], by = list(my_DF$YEAR, my_DF$MONTH, my_DF$ID), median)

In this way I obtain the values I wanted, but, of course, this just create a new dataframe. I'm failing in finding a rapid way to paste the values of the dataframe "agg" in a new column of dataframe "my_DF", basing on the YEAR, MONTH and ID corrispondence.

For instance, I want obtain a thing like:

        YEAR     MONTH       ID   LENGHT   MONTHLY_LENGHT_MEDIAN
1       2000     january      S1   0.2           0.2
2       2000     january      S1   0.3           0.2
3       2000     january      S1   0.1           0.2
4       2000     january      S2   0.5           0.4
5       2000     january      S2   0.3           0.4
6       2000     february     S1   0.9           0.6
7       2000     february     S1   0.4           0.6
8       2000     february     S1   0.6           0.6
9       2000     february     S3   0.4           0.35
10      2000     february     S3   0.3           0.35
11      2000     march        S1   0.7           0.7

So, I'm wondering if a conditional command is suitable in my case (if, ifelse...).
Unfortunately, I'm not good with these commands... How could I do? Thanks for helping!