The אבודרהם in Hilchos Shabbos writes that the minhag in all of צרפת ופרובינצא is that after each person finishes his קריאה the chazzan tells him in a loud voice חזק. The source for this is the Midrash Rabbah who explains the passuk in יהושע. The passuk says לא ימוש ספר התורה הזה מפיך – the word הזה means that יהושע was holding the ספר תורה and Hashem told him חזק ואמץ. The בית יוסף at the end of ,סימן קל”ט also brings this Midrash Rabbah.
We learn from here two things. Firstly, there is a מעלה of holding the ספר תורה. Therefore one should hold onto the ספר תורה when he is making the ברכה. [The Mishna Berurah brings from the ב”ח and ט”ז that one should also hold onto the ספר תורה during the קריאה.] Secondly, when one is מסייםthe Torah we say to him חזק, just like Hashem told יהושע when he was holding the ספר תורה. The רמ”א (סימן קל”ט סעיף י”א) brings both of these מנהגים.
There are two ways to understand this מנהג. Either it means that after each עולה we say חזק which today is the מנהג of the ספרדים. Or, it means only after the last עולה. The אבודרהם says that the מנהג of ספרד was to say it by the last עולה of every חומש. This is today the מנהג of the אשכנזים. The אליה רבה brings from the מהר”ם מינץ that the minhag to say it after each חומש is because it is like a הדרן on a מסכת, that you should not forget what you learned.
It also seems that there were different מנהגים who would say חזק. The אבודרהם says the חזן would say it. The אורחות חיים brought in the בית יוסף says אומרים לו we say to him which means the whole ציבור says it.
There are also different מנהגים in the נוסח of what is said. The כף החיים says the minhag is to say חזק וברוך. This נוסח is mentioned in the אבודרהם and the כנסת הגדולה. The minhag of the אשכנזים is to say חזק חזק ונתחזק. The אליה רבה and the חתם סופר both say that the proper נוסח is חזק חזק חזק which is the גימטריא of משה. The ערוך השלחן rules that this is the proper נוסח. However the accepted minhag is to say חזק חזק ונתחזק.
All the poskim say that the עולה himself should not say חזק. Besides for the fact that everyone is telling him חזק it is also a הפסק between the קריאה and the ברכה. Rav Henkin zt”l however rules that the עולה may also say it if he wants. This was also the minhag of the Steipler zt”l. According to everyone בדיעבד it is not considered a הפסק. [1]
Prepared by R’ Avrohom Yehoshua Ziskind
[1] Sources;הקריאה בתורה והלכותיה,ספר יגל יעקב,גבורות אליהו,פסקי תשובות