According to the ESA/390 Principles of Operation (SA22-7201-08), relative 
addressing instructions were introduced in 1996. 

Relative-long instructions were added in 2000.

Under "Highlights of ESA/390", p. 1-3:

"The immediate-and-relative-instruction facility includes 13 new instructions, 
most of which use a halfword-immediate value for either signed-binary 
arithmetic operations or relative branching. The facility reduces the need for 
general registers, and, in particular, it eliminates the need to use general 
registers to address branch targets. As a result, the general registers and 
access registers can be allocated more efficiently in programs that require 
many registers. (September, 1996)"

Also under "Highlights...", p- 1-5:

"Certain new z/Architecture instructions are available on a model in the 
ESA/390 architectural mode when z/Architecture is installed. These new 
instructions are highlighted as follows:
...
– BRANCH RELATIVE AND SAVE LONG and BRANCH RELATIVE ON CONDITION LONG are like 
the BRANCH RELATIVE AND SAVE and BRANCH RELATIVE ON CONDITION instructions 
except that the new instructions use a 32-bit immediate field. This increases 
the target range available through relative branching... (October, 2000)"

Under "Summary of changes in Fourth Edition":

    The instructions of the immediate and relative-instruction facility are 
added.
    These are:
    ...
    - BRANCH RELATIVE AND SAVE
    - BRANCH RELATIVE ON CONDITION
    - BRANCH RELATIVE ON COUNT
    - BRANCH RELATIVE ON INDEX HIGH
    - BRANCH RELATIVE ON INDEX LOW OR EQUAL
    ...

Also, under "Summary of changes in Eighth Edition":

    The following new instructions that have been placed in both z/Architecture 
and ESA/390 are added:
    ...
    - BRANCH RELATIVE AND SAVE LONG
    - BRANCH RELATIVE ON CONDITION LONG
    ...
    - LOAD ADDRESS RELATIVE LONG

Looking at the dates, the first machine to support relative addressing (but not 
relative-long) was (this is a guess) the IBM 9672 G3 (announced in 1996) or G4 
(1997).

All z/Architecture machines, starting with the z900 (announced October 2000), 
support relative addressing.

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