Combine Pandas DataFrame DateTime Columns

Better use pd.to_datetime:

df['Date'] = pd.to_datetime(df[['Year','Month','Day']])
>>> df
   Year  Month  Day       Date
0  2003      1    8 2003-01-08
1  2003      2    7 2003-02-07

>>> from datetime import datetime
>>> df['Date'] = df.apply(lambda row: datetime(
                              row['Year'], row['Month'], row['Day']), axis=1)
>>> df
   Year  Month  Day                Date
0  2003      1    8 2003-01-08 00:00:00
1  2003      2    7 2003-02-07 00:00:00

Update 2020-03-12: The answer from sacul is better and faster:

%%timeit
df.apply(lambda row: datetime(
                              row['Year'], row['Month'], row['Day']), axis=1)

2.53 s ± 169 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

# use below, above is slow!!!
%%timeit
pd.to_datetime(df[['Year','Month','Day']])

14.4 ms ± 3.37 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)