You will have to cut a "saddle" into the cross piece. Basicaly, you can use the tubing as a scribe, mark the diameter onto the cross piece at one end, )it should look like a half moon at the end of the pipe(, mark the center, now turn the pipe over and do the same. After you have your marks, cut out the half moons. This should give you a "saddle" appearance and should be a fairly close match to the diameter of the pipe your welding to.
If you have enough pipe you can cut off about 1 inch and use that as a scribe piece, just lay it on the end of the pipe you want to cut with half of the scribe past the end of the pipe your gong to "saddle".
Then you can check the fit and remove any high spots/slag to get a tight fit. Weld.
Sounds harder than it is, play with it and it will make sense.
You could also "mash" the end like you see on farm gates and stock panels but saddled looks better.