Part of what makes a transition effective, lies in the time it takes to do it. The first song is upbeat with a quicker tempo. The second one is a slower tempo worship song. Obviously, I'm gonna assume that you're going to be slowing down the last part of the song "Lord I lift Your Name on High" which is in the key of "F".
Don't be in a rush to leave that key just yet, allow the people to continue praising and declaring His goodness.
In that time of praise, I would be highlighting certain notes. In this case, in would be the "F" and the "C" notes. Here's why ... In the transition, I'll be using a chord which contains these notes. So although the chord and the key is now changing, there is a sound that can still be heard that is common to both the old and the new key, (that's why I like to use 11ths, and 13ths chords).
That makes for a smoother, flowing transition.
When you're ready to make the transition, here it is, short and sweet:
F C / F A
C Old key of "F"
Eb Bb Db /
F Ab
C (Eb13) Transition chord (Notice the
"F" and
"C" are still present)
Eb Bb Db / Eb G
Bb (Eb7) 5th of new key, which is "Ab" (Notice that although the right hand notes have changed, the left hand notes are still the same. This gives stability during the transition.)
Ab Eb Ab / C Eb
Ab (Ab) New key
The top notes moving down, ("C", "Bb", and "Ab"), allows the congregation to hear a definite yet subtle change in keys.
This is one way I might make the transition between songs, as T-Block mentioned, there are countless others.
I also believe that sometimes, just gradually slowing down and coming to a stop, and not rushing, but allowing the people to worship Him before starting in the new key. Now
that also can be
very effective.
I know it's kind of lengthy, but the object is to learn how to make transitions between songs, and not just these two songs. Hope this helps you .... God bless

BroAllan