The problem is, like viewed in the others answers, a problem of memory. And a solution is to store data on disk, then  to build an unique dataframe.
With such huge data, performance is an issue.
csv solutions are very slow, since conversion in text mode occurs.
HDF5 solutions are shorter, more elegant and faster since using binary mode.
I propose a third way in binary mode, with pickle, which seems to be even faster, but more technical and needing some more room. And a fourth, by hand.
Here the code:
import numpy as np
import pandas as pd
import os
import pickle
# a DataFrame factory:
dfs=[]
for i in range(10):
    dfs.append(pd.DataFrame(np.empty((10**5,4)),columns=range(4)))
    
# a csv solution
def bycsv(dfs):
    md,hd='w',True
    for df in dfs:
        df.to_csv('df_all.csv',mode=md,header=hd,index=None)
        md,hd='a',False
    #del dfs
    df_all=pd.read_csv('df_all.csv',index_col=None)
    os.remove('df_all.csv') 
    return df_all    
    
Better solutions :
def byHDF(dfs):
    store=pd.HDFStore('df_all.h5')
    for df in dfs:
        store.append('df',df,data_columns=list('0123'))
    #del dfs
    df=store.select('df')
    store.close()
    os.remove('df_all.h5')
    return df
def bypickle(dfs):
    c=[]
    with open('df_all.pkl','ab') as f:
        for df in dfs:
            pickle.dump(df,f)
            c.append(len(df))    
    #del dfs
    with open('df_all.pkl','rb') as f:
        df_all=pickle.load(f)
        offset=len(df_all)
        df_all=df_all.append(pd.DataFrame(np.empty(sum(c[1:])*4).reshape(-1,4)))
        
        for size in c[1:]:
            df=pickle.load(f)
            df_all.iloc[offset:offset+size]=df.values 
            offset+=size
    os.remove('df_all.pkl')
    return df_all
    
For homogeneous dataframes, we can do even better :
def byhand(dfs):
    mtot=0
    with open('df_all.bin','wb') as f:
        for df in dfs:
            m,n =df.shape
            mtot += m
            f.write(df.values.tobytes())
            typ=df.values.dtype                
    #del dfs
    with open('df_all.bin','rb') as f:
        buffer=f.read()
        data=np.frombuffer(buffer,dtype=typ).reshape(mtot,n)
        df_all=pd.DataFrame(data=data,columns=list(range(n))) 
    os.remove('df_all.bin')
    return df_all
And some tests on (little, 32 Mb) data to compare performance. you have to multiply by about 128 for 4 Gb.
In [92]: %time w=bycsv(dfs)
Wall time: 8.06 s
In [93]: %time x=byHDF(dfs)
Wall time: 547 ms
In [94]: %time v=bypickle(dfs)
Wall time: 219 ms
In [95]: %time y=byhand(dfs)
Wall time: 109 ms
A check :
In [195]: (x.values==w.values).all()
Out[195]: True
In [196]: (x.values==v.values).all()
Out[196]: True
In [197]: (x.values==y.values).all()
Out[196]: True
            
Of course all of that must be improved and tuned to fit your problem.
For exemple  df3 can be split in chuncks of size 'total_memory_size - df_total_size' to be able to run bypickle.
I can edit it if you give more information on your data structure and size if you want. Beautiful question !