1 Kings 11:29 (KJV)
And it came to pass at that time when Jeroboam went out of Jerusalem, that the prophet Ahijah the Shilonite found him in the way; and he had clad himself with a new garment; and they two were alone in the field:
וַֽיְהִי בָּעֵת הַהִיא וְיָֽרָבְעָם יָצָא מִירוּשָׁלִָם וַיִּמְצָא אֹתוֹ אֲחִיָּה הַשִּׁילֹנִי הַנָּבִיא בַּדֶּרֶךְ וְהוּא מִתְכַּסֶּה בְּשַׂלְמָה חֲדָשָׁה וּשְׁנֵיהֶם לְבַדָּם בַּשָּׂדֶֽה
- וְהוּא - and he
- מִתְכַּסֶּה - had clad himself
- בְּשַׂלְמָה - with a garment
- חֲדָשָׁה - new
Ahijah was the last one mentioned and was the last one actively doing something (finding Jeroboam). So this would indicate Ahijah was wearing the new garment. Other translations such as the NASB remove the ambiguity by explicitly stating Ahijah was wearing it.
This is disputed by some who think Jeroboam was wearing the garment, though Carl Keil calls this view erroneous.
There's not any real significance to this act if Jeroboam had been wearing the garment. The garment represented the kingdom, which Jeroboam did not yet possess. The kingdom ultimately belonged to God, who appointed kings to rule it through His prophets. Reference Jeremiah 1:9-10 (NKJV):
9 Then the Lord put forth His hand and touched my mouth, and the Lord said to me:
“Behold, I have put My words in your mouth.
10 See, I have this day set you over the nations and over the kingdoms,
To root out and to pull down,
To destroy and to throw down,
To build and to plant.”
The authority over kingdoms belonged to God, who then gave Jeremiah that authority.
In the same way, the prophet Ahijah was given the authority to give Jeroboam 10 tribes. The new, whole garment signified the whole kingdom of Israel. Ahijah took the garment off himself, tore it in 12 pieces, and gave 10 pieces to Jeroboam.
1 Kings 11:30 (KJV)
and Ahijah caught the new garment that was on him, and rent it in twelve pieces:
Then Ahijah took hold of the new garment that was on him, and tore it into twelve pieces.
וַיִּתְפֹּשׂ אֲחִיָּה בַּשַּׂלְמָה הַחֲדָשָׁה אֲשֶׁר עָלָיו וַיִּקְרָעֶהָ שְׁנֵים עָשָׂר קְרָעִֽים
- אֲשֶׁר - that
- עָלָיו - [was] on him
This is a normal way of expressing that the garment was on Ahijah. Compare this to
2 Samuel 13:19 (KJV)
And Tamar put ashes on her head, and rent her garment of divers colours that was on her, and laid her hand on her head, and went on crying.
Then Tamar put ashes on her head, and tore her robe of many colors that was on her, and laid her hand on her head and went away crying bitterly.
וַתִּקַּח תָּמָר אֵפֶר עַל־רֹאשָׁהּ וּכְתֹנֶת הַפַּסִּים אֲשֶׁר עָלֶיהָ קָרָעָה וַתָּשֶׂם יָדָהּ עַל־רֹאשָׁהּ וַתֵּלֶךְ הָלֹוךְ וְזָעָֽקָה
- אֲשֶׁר - that
- עָלֶיהָ - [was] on her
This is the feminine form of the same phrase. Even though it's very clear from the previous verse that she was wearing the robe, the phrase “that was on her” is still used as a normal way of expressing that the robe was on Tamar.
1 Samuel 18:4 (KJV)
And Jonathan stripped himself of the robe that was upon him, and gave it to David, and his garments, even to his sword, and to his bow, and to his girdle.
And Jonathan took off the robe that was on him and gave it to David, with his armor, even to his sword and his bow and his belt.
וַיִּתְפַּשֵּׁט יְהֹונָתָן אֶֽת־הַמְּעִיל אֲשֶׁר עָלָיו וַֽיִּתְּנֵהוּ לְדָוִד וּמַדָּיו וְעַד־חַרְבֹּו וְעַד־קַשְׁתֹּו וְעַד־חֲגֹרֹֽו
- אֲשֶׁר - that
- עָלָיו - [was] upon him (KJV) / [was] on him (NKJV)
The main difference here being the word form for “stripped” being reflexive (וַיִּתְפַּשֵּׁט = and he stripped himself), which removes any possible ambiguity of who “was upon him” would refer to (plus the obvious fact it was then given to David). But this can't really occur with 1 Kings 11:30, because Ahijah isn't taking hold of himself, he's taking hold of the garment that was on him[self]. The garment represented the kingdom that was almost fully torn away from Solomon and given to another.
A somewhat similar figurative act occurred with the prophet Samuel's garment in 1 Samuel 15:26-28 (NKJV):
26 But Samuel said to Saul, “I will not return with you, for you have rejected the word of the Lord, and the Lord has rejected you from being king over Israel.”
27 And as Samuel turned around to go away, Saul seized the edge of his robe, and it tore. 28 So Samuel said to him, “The Lord has torn the kingdom of Israel from you today, and has given it to a neighbor of yours, who is better than you.
The garment upon Samuel represented the kingdom, which, though Saul tried to grasp it again, was torn away from him.