The simple answer is that the eidei kiddushin witness the chupa, bideken and yichud, which between them constitute nissuin too.
However, there is very convincing argument that nissuin does not require eidim lkiyum. Although by all chaluyos of dovor sh'berva we need eidim lkiyum (like gerushin and kiddushin, and others), there are two reasons why nissuin is different:
1) The Gemara in Kiddushin 65a writes that using the concept of hoda'as baal din k'meah eidim dami, one can circumvent the requirement for eidim, and the Kiddushin would theoretically be valid without eidim. (It is beyond the scope of this answer to explain how the two concept are interlinked). The reason the Gemara gives why this doesn't work is because when it is chav l'acheirim - detrimental to others - the concept of hoda'as baal din does not apply. Kiddushin is considered chav l'acheirim [either because the marriage causes the woman to become forbidden to all others, or because it causes him/her to become forbidden to each other's realtives - see Rashi & Rashba Kiddushin 65). Nissuin, however, is not chav l'acheirim, because both the relatives and the rest of the world are all already forbidden with the Kiddushin.
2) According to some (notably, R' Chaim Solovetzik), the requirement for eidi kiyum is only by a 'chalos ha'adam' (in Achronistic parlance), not by a 'chalos hatorah'. Nissuin is considered a chalos hatorah, and therefore does not require eidim lkiyum.
Therefore, some Poskim (e.g. Or Someach, linked by @JoelK) do not require eidim by Nissuin.
Nevertheless, the Avnei Miluim (37:18) and HaMakneh (EH §50) rule that it is required. The simple reading of the Tosfos Ri Hazaken in Kiddushin 10a is that Nissuin does require eidim.