Exegesis:

kai estai … soi lit. ‘and there will be for you.’ The meaning depends on whether chara kai agalliasis ‘joy and exultation’ (understood as one concept, see below) is (1) subject of estai or (2) predicate with it. When subject the meaning of estai … soi amounts to “you will have” (Revised Standard Version, Translator’s New Testament, Bible de Jérusalem, Menge) or ‘will be your share’ (Nieuwe Vertaling, Rengstorf). When chara kai agalliasis is predicate, the subject is either ‘he,’ i.e. John (The Four Gospels – a New Translation, Brouwer, La Sainte Bible: Nouvelle version Segond révisée), or ‘this’ (An American Translation, Phillips) or ‘it’ (Moffatt) referring both to the announced birth. On the whole the former is the more acceptable interpretation.

chara kai agalliasis ‘joy and exultation,’ best understood as expressing one concept, each word strengthening the other; hence New English Bible, “your heart will thrill with joy”.

chara ‘joy’ the more general word.

agalliasis ‘exultation,’ often with a religious connotation and, therefore, stronger than chara, as brought out by Willibrord, Zürcher Bibel (‘joy and exultation’), cf. also the verb agalliaomai ‘to exult’ (1.47; 10.21; 1 Pet. 1.6, 8). But because of the fact that chara and agalliasis go so closely together most translators do not differentiate sharply between them, cf. “joy and gladness” (Revised Standard Version), “gladness and delight” (An American Translation), “joy and delight” (Translator’s New Testament).

kai polloi … charēsontai ‘and many will be glad.’ kai is slightly ascensive: not only you yourself will be glad but also many other people. There is no indication in the text to whom polloi refers.

chairō ‘rejoice,’ ‘be glad,’ a very common word.

epi tē genesei autou ‘at his birth,’ epi with dative indicates the cause of the gladness.

genesis ‘birth.’

Translation:

You will have joy and gladness, or, ‘you will rejoice and exult,’ ‘you will be happy, very truly you will be happy’ (Shipibo-Conibo; similar emphatic repetition in Navajo, Apache); or, ‘you will have great joy’ (Tagalog), ‘you will take-in (lit. eat) a very true pleasure’ (Sranan Tongo), ‘you being very happy will be overwhelmed’ (Ekari). For close synonyms joy (also in 1.44; 2.10; 6.23; 8.13; 10.17; 15.7, 10; 24.41, 52) and gladness (cf. also 15.16, 32; 22.5; 23.8); still other languages use expressions built on ‘happiness of life’ (Western Highland Purepecha), ‘to like’ (Huehuetla Tepehua), ‘the being lifted up of the heart’ (Tae’), ‘warmth of the heart’ (Batak Toba).

Rejoice (also in 1.47, 58; 6.23; 10.20f; 13.7; 15.5f, 8; 19.37), i.e. to have, or feel, or show joy, for which see above.

At his birth often is better rendered, ‘that/because he was born,’ or made the subject of a causative verb, e.g. ‘his birth will cause many to rejoice.’ Such a restructuring may also affect the first line, because of the existing parallelism between the two, e.g. ‘his birth will completely cause-happiness to you, and cause-happiness to many people’ (Pampanga).

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.