To summarize the above, you, as a gift receiver are not required to report or pay taxes on gifts you received. The giver of the gift pays any tax due. However, the giver will not be subject to any tax until the total of all reportable gifts surpasses $5,490,000 (2017 lifetime inclusion amount).
The annual federal gift tax exclusion allows you to give away up to $14,000 in 2017 to as many people as you wish without those gifts counting against your $5.49 million lifetime exemption. (After 2017, the $14,000 exclusion may be increased for inflation.)
The following articles give examples of how this works. In your situation, if your boyfriend gifts you 14,000 or less, nothing gets reported and his lifetime inclusion remains at $5.49 million. If he gifts you 15,000, he would complete a gift tax return which would reduce his lifetime inclusion by $1K to $5,489,000, meaning he can still gift that amount before paying any tax.
